When can one make up a missed prayer?
The Shulhan Aruch (O.H. 108) delineates the rules regarding one who missed the Amida prayer. In the times of the Bet Hamikdash, if one failed to bring an offering, one was able to bring a compensatory offering. Similarly, if one did not recite the Amida for one of the three daily prayers, one can make it up later. The first rule is that if one missed the Amida, one can make it up by reciting an extra Amida at the next prayer. For example, if one did not recite the Amida of Shaharit, one could make it up during the next prayer service, Minha. Furthermore, one can only make it up during the prayer service that immediately follows that which one missed. Thus, if one missed Shaharit, one cannot make it up during Arvit, for example. Secondly, the prayer that one is making up for must be recited after one recites the regularly scheduled prayer first. So if one missed Shaharit, when the time for Minha would come, one would first have the intention that the first Amida would be for Minha, and then one would recite an Amida again afterwards to make up for Shaharit. One exception to this is Musaf, which, if one missed, one may not make up. Musaf may be recited up until sunset and therefore the next prayer in which one would theoretically be able to make it up would be Arvit. Nevertheless, the Tosafot explain that since Musaf has references to bringing offerings and offerings are never brought at night, it would not be proper to recite it during Arvit.
It must be noted that one can only make up a prayer that was missed unintentionally (Shogeg), not intentionally (Mezid). What constitutes Mezid and Shogeg in this context is not black and white and there are cases in which one “intentionally” misses a prayer but it may still be considered Shoged. The Shulhan Aruch (ibid:8) says that if one was busy in one’s affairs and thought that one would have enough time to pray afterwards but ended up missing the time for prayer, such a situation would be considered Shogeg and one would be able to make up the prayer. Similarly, if one missed a prayer because one was involved in a business transaction that was meant to prevent a financial loss, one would be able to make up the prayer later on.
The Biur Halacha (cf. Mihu Lechatechila), citing the Pri Megadim, specifies that if one stands to lose one fifth of one’s net worth, one could skip a prayer to prevent it and make up the prayer later. Conversely, the Mishna Berura (M.B., O.H. 104:2) says that if one is in the middle of the Amida, no type of potential monetary loss warrants one stopping in the middle of the prayer in order to resolve the financial matter, since this is a slight to the honor of the prayer.
Summary: If one misses a prayer, one may make it up according to specific Halachic parameters.