Salam Alaikum. I want to know if there is a limit to the number of times one can have intercourse with one's wife in one night at a time: once, twice, or as much as one wants till satisfied.
Wa Alaikum As Salam. No. There are no Islamic texts that limit a husband/wife on how many specific times they can have intercourse in a night. They can have sex as many times as they want. The only guidelines are the two following: (1) Minimally, they should fulfill each other's desires and not deprive the other of their right to sex. (2) Maximally, neither of the partners should be harmed as a result of sex. For example, if you have intercourse multiple times but want to have more but it will harm the wife then you should not do so until she recovers and can go on.
While Insight gave a good answer, I would add that even though there is no strict limit in the text, I would also put each spouse's wishes itself as a limit. So for example if the couple had sex a certain number of times after which the wife said she has had enough, the husband should respect her wishes. This is part of good character and being good to your spouse which has been specifically commanded in the text.
The quran doesn't state a number, it just say's:
Your wives are a place of sowing of seed for you, so come to your place of cultivation however you wish and put forth [righteousness] for yourselves. And fear Allah and know that you will meet Him. And give good tidings to the believers (2:223)
so having sex in a legal way (you may not have intercourse with a woman which is not your wife), and state (you may not have intercourse during menses for example which is the topic of the verse before) is allowed, without clear limitation.
From a linguistic perspective we may also interpret the verse as saying "whenever you want as long as they are in a clean state", this is a view which is rarely discussed in tafssir books (the focus on the tafssir of the word أنى is on the place or location, based on ahadith and tradtions about positions for intercourse or "anal sex"), but quoted by ibn 'Ashur in his tafssir at-Tahrir wa tanwir:
فتحمل ( أنى ) على معنى " متى " ويكون المعنى : فأتوا نساءكم متى شئتم إذا تطهرن
He also quoted Lissan al-'Arab:
وقال في لسان العرب : إن ( أنى ) تكون بمعنى ( متى )
Where أنى has among it synonyms متى (when, at what time?).
The quran also mentions three time recommendations where one should/could have intercourse (24:58).
As أنى in Arabic means wherever (in questions from where? see for example 2:247) if it is related to a location, or to whatever (in questions when?) when it is related to a time. In a more general use it means "how?".
In the hadith we may read:
When anyone amongst you has sexual intercourse with his wife and then he intends to repeat it, he should perform ablution. (sahih Mulsim, Jami' at-Tirmdihi and in the sunan of ibn Majah and abi Dawod)
which is a legal permission to re-have intercourse. (see also islamqa #169627)
The only limitation is your capability and the order to not harm yourself or your wife, so none of you should insist on having sex several times if it may hurt any of you and you should respect each others needs and desires.
And live with them in kindness. (4:19)
A husband also must be aware that among his duties towards his wife there's the necessity to satisfy her (sexual) needs.
Also read islamqa #1078.