Gemara

29b (Mishnah - R. Meir): If wine of a Yisrael was Kanus (put) in a pouch or bottle of a Nochri, one may not benefit from it;

Chachamim say, one may not drink it, but one may benefit from it.

74b (Beraisa - Rebbi): It suffices to dry a Gas, bucket (used to draw wine from the Gas) or funnel (all made of earthenware) of a Nochri;

Chachamim forbid.

Rebbi agrees that a Nochri's bottles are forbidden.

This is because people leave wine in bottles for a long time.

75b (Beraisa): If a used Keli of a Nochri was used with cold food, e.g. cups and flasks, and a Yisrael used it before Kashering, the food is forbidden;

Contradiction (Beraisa #2): The food is permitted.

Resolution: They argue about whether Nosen Ta'am li'Fgam (a detrimental absorbed taste, e.g. after 24 hours) forbids.

Question: According to the opinion that permits Nosen Ta'am li'Fgam, why must one Kasher Kelim of Nochrim for use after that day?

Answer: Chachamim decreed to Kasher them, lest they will be used the same day.

Chulin 108a - Suggestion: Because meat and milk is a Chidush, we do not learn from it (to forbid what absorbed taste from an Isur that is not intact).

Pesachim 44b: It is a Chidush, for if one soaks them together the entire day they are permitted, but if they are cooked together, they are forbidden.

Rishonim

Rambam (Hilchos Ma'achalos Asuros 17:4): If one needed to Kasher a Keli and used it before Kashering it, the food it permitted, for any absorbed fat is Nosen Ta'am li'Fgam.

Rosh (Avodah Zarah 2:20): Rashi explains that wine of Yisrael was put in Nochri Kelim for a long time. This implies that it is not forbidden immediately. The text of the Gemara forced him to say so. (It says that wine of Yisrael was Kanus, i.e. entered in them, and not simply 'was put in Nochri Kelim.) Also, it is unreasonable to say that absorptions in the walls of the Keli enter the wine immediately. We say so only about something heated on a fire, but not about cold things. Even if we would say that absorptions enter the wine immediately, we could understand the law only according to Rashi, who says that any amount of Stam wine of Nochrim forbids, but not according to R. Tam, without says that it is Batel in 60 parts of Heter, even Min b'Mino (when mixed with its own kind, i.e. wine). We cannot say that all the absorptions immediately enter the wine! We could explain Rashi to say that it is forbidden immediately. I.e. this was a decree, just like we decree to immediately forbid a Yisrael's Keli in which wine of Nochrim was put with intent to leave it for a long time (74b). In both cases, we decree lest it be left in for a long time. Rashi does not connote like this. Even if Rashi means this, he does not forbid immediately if wine of Yisrael was put in Nochri flasks, which Bahag says are normally are not used to store for a long time. However, Rashi did not specify how long it must stay in to become forbidden. It seems that it must be inside for 24 hours. When two cold things are together, Pleitah (giving off absorbed tastes) or absorption occurs after 24 hours. We say that meat and milk is a Chidush, for if one soaks meat in milk the entire day it is permitted, but if they are cooked together, it is forbidden. Why is this a Chidush? Also other Isurim transfer to Heter only if cooked! Rather, other Isurim transfer to Heter if left together for a full day of 24 hours, as if they were cooked together. This is Kavush (pickling), which the Gemara equates to cooking. Regarding meat and milk, the Torah forbids only if they were (truly) cooked together. Similarly, if wine was in a Keli for 24 hours, the walls of the Keli are Polet all the wine (absorbed) in them, and this forbids the wine, even according to R. Tam who says that it is Batel in 60 parts of Heter. A partial proof is from Iruy (Kashering by leaving water in a Keli for 24 hours, three times). The water makes the Kelim be Polet whatever it can in 24 hours, but not in less than 24 hours. I heard that Avi ha'Ezri inferred from Rashi that Chachamim permit drinking the wine if it was not put in for a long time, like R. Shimon ben Guda's testimony that Raban Gamliel drank wine of a Yisrael that was put in a small flask. We are stringent because Chachamim did not accept the testimony.

Rosh (23): The Halachah follows Rava and Ravina (who permit putting beer in a Nochri's Keli - 33b), for they are Basrai. One may put also water in Nochri flasks, even though we estimate based on the the entire volume of the Keli (perhaps it is full of absorbed Isur) and there is not 60 times as much water or beer. This is because the taste of wine it absorbs is Pagum (spolied) from the beginning. The Halachah is, bottles of Nochrim are permitted after 12 months.

Rosh (Teshuvah 19:4): Some permit Nochrim Kelim in which they put wine in the last 12 months, because (only the inner layer of the wall absorbs, and) one puts more than 60 times as much liquid in them than the amount of Isur absorbed in the layer. They permit putting wine in l'Chatchilah. Isur leaves the walls, is mixed with Heter and is Batel in it, and the walls absorb Heter. Surely this purges more Isur than leaving it 12 months without using it!

Beis Yosef (YD 137 DH Kasav ha'Rosh): The Mordechai (Avodah Zarah 858) says similarly, and Orchos Chayim in the name of R. Peretz, and the Ri relied on this in practice. How will they explain the Mishnah (that forbids the wine)? Perhaps this is when there is less than 60 times as much wine as the inner layer. However, the Halachah follows the opinion that any amount of wine of Nochrim forbids.

Poskim

Shulchan Aruch (YD 137:1): If wine of Yisrael was put in a Keli forbidden due to wine of Nochrim before it was Kashered, one may not drink the wine, but one may benefit from it. This is even if the Keli is dry, unless 12 months passed.

Beis Yosef (DH u'Mah she'Chosav Afilu): The Tur requires waiting 12 months, to teach unlike the Ramban (Hashmatah in Ramban ha'Shalem), who permits wine that was put in a forbidden cup before Kashering if it was not a Ben Yomo (used for Isur in the last 24 hours). He learns from the Beraisa that permits due to Nosen Ta'am li'Fgam. The Ran (40a DH v'Chulan) said that the Ramban said so only l'Halachah, but not to be followed in practice. The Rosh (Teshuvah 19:6) says that surely someone else wrote this in the name of the Ramban, for we permit Nosen Ta'am li'Fgam for cooked foods, but not for wine. However, he concluded that if the Kelim were dry, the wine is permitted if it was not inside for 24 hours.

Taz (1): The Rosh in Teshuvah 19:6 says that since wine is not put in such Kelim for a long time, if it was dry and one used it, the wine is permitted. This is even if it was in for 24 hours, unlike the Beis Yosef. However, the Tur says that the Rosh forbids! It seems that this is when the Keli needed Iruy for three days, but if it merely needed to be rinsed, there is no Isur inside and it does not forbid. The Ramban permits only for Kelim like funnels, in which wine never stays. He holds that any amount of Stam wine of Nochrim forbids, but we hold that it is Batel in 60. One may rely on the lenient opinions for mid'Rabanan matters like this, especially since we are lenient about Stam wine of Nochrim when there is even a small (reason for) Heter, and especially about absorptions.

Gra (2): The Ramban explains 'Kelim in which wine is not put for a long time', i.e. it cannot be put in for a long time, e.g. a funnel.

Shach (2): We do not distinguish a Nochri's Keli from a Yisrael's Keli that absorbed Yayin Nesech.

Shach (3): Any wine that one may benefit from is Batel in 60. However, here the wine was Isur Hana'ah before it was absorbed in the Kelim, so it is not Batel. It does not forbid Hana'ah from the Heter wine that is put in the Keli later, for a mere taste of it mixes, and this has no value. However, the Ro'oh says that it is Batel, for it does not forbid Hana'ah. The Shulchan Aruch holds like I said.

Gra (1): We forbade to make a saddle out of a Nochri wine pouch, lest the Yisrael tear off part of the saddle to patch his own pouch (and his wine will absorb from the Nochri's wine), even though it is dry.

Rema: If it is a Keli in which wine is put in for a long time, it is forbidden immediately.

Shulchan Aruch (ibid): If it is a Keli in which wine is not put for a long time (and it is dry), the Yisrael's wine is forbidden only after 24 hours.

Beis Yosef (DH u'Mihu): If the Keli was so wet that something that touched it could wet something else, it forbids (immediately) what is put inside. R. Yerucham says that if wine is not put in a Keli for a long time, and a Nochri used it and it dried and a Yisrael used it without rinsing, it is permitted. L'Chatchilah, one must rinse it first.