The Missing MussafTwo laws concerning the Mussaf service we say on Shabbos and festivals are derived from the laws governing the offering of the additional (Mussaf) sacrifice on festivals.
"These are the festivals of Hashem ... to offer sacrifices ... each daily one on its day." (Vayikra 23:37)
The double expression of "day" teaches us that the Mussaf sacrifice may be offered throughout the entire day, and that if the kohanim failed to offer it on its designated day there is no responsibility to offer a compensation for it on the next day.
This is the basis for the ruling of the Shulchan Aruch (Orach Chaim 286:1), that although one should strive to say the Mussaf service on Shabbos and festivals before the end of the seventh hour after sunrise (because the Mussaf sacrifice was preferably offered before that time), he fulfills his duty even if he says it later in the day. But, if he failed to say it before the end of that day he cannot compensate by saying the next prayer service twice, as he can do in regard to any other missed prayer services. The reason for this is that even though our three daily services correspond to the daily sacrifices, there is no specific mention in them of the sacrifice which they represent, and are therefore not bound by the rule which makes compensation for a communal sacrifice impossible. In the Mussaf service, however, we specifically mention the sacrifice it represents, and is therefore subject to the rule governing that sacrifice which says that no compensation can be offered if it was missed.
The Shulchan Aruch (ibid. 286:4) discusses the problem arising when one delays the Mussaf service until the time for the Mincha service (6 hours after sunrise) arrives, and distinguishes between what a congregation does in such a situation (always saying Mussaf first) and what an individual does (in some situations saying Mincha first because it is more regular than Mussaf). An interesting question arises in regard to one who finds himself with only enough time left before sunset to say either Mussaf or Mincha. One view of the authorities is that he should say Mussaf which cannot be compensated for and skip Mincha which he can compensate for by saying Maariv twice. Other authorities, however, challenge this and rule that Mincha takes precedence even if Mussaf is altogether missed, because it is more regularly prayed than Mussaf.
A Four-Legged Armed RobberOnce there was a very pious Jew who was very ill and the physicians said that his only cure was to drink hot, fresh milk directly from a goat each morning. So a goat was brought one day and tied to his bed so that he could have this cure. The next day his colleagues came to visit him. As soon as they saw the goat they exclaimed: "An armed robber is in this house (a small domesticated animal such as a goat is impossible to properly guard and it goes pasturing in the fields of others - Rashi) and we are coming to visit!" They thereupon turned around and left. When this pious Jew eventually passed away his colleagues reviewed his life and found that he had committed no other sin in his lifetime aside from maintaining the goat. He too declared on his deathbed: "I know that the only sin I ever committed was in regard to that goat when I violated the command of my colleagues, for the Sages have ruled that it is forbidden to raise small domesticated animals in Eretz Yisrael."
The problem raised by this story is that except for idolatry, adultery, incest and murder, all Torah prohibitions are put aside for the saving of a life. An approach to solving this problem is suggested by Hameiri who states that in a situation where the Sages have decreed something to protect the public, it is proper for a pious Jew to even sacrifice his life in order to abide by it.
Another approach may be suggested based on a position taken in the responsa of the great 19th century German Torah authority Rabbi Yaakov Ettlinger (Responsa Binyan Zion 167-171) that there is a dispute amongst Talmudic Sages and early commentaries as to whether one may steal from another in order to save his own life. The halachic ruling we follow is that it is permissible, but it may be that the visiting sages in the above story held the position that it is forbidden. (But why did Rabbi Ettlinger fail to mention this source as a support for his position?)