Eggiweg is pretty close to the answer. The vintage Tamagotchis don't age based on time but rather every time they wake up they go up a year or, as Eggiweg has precisely put it, every time they pass 12 a.m. (or should have). Additionally, vintage Tamagotchis have an internal clock that determines how long they will live which can be manipulated so that how much time they have lived is no longer consistent with real time. This is done by changing the clock to a later time and the internal clock will continue counting down from the new time instead of thinking it has actually ran for all that time. For example, say a P1 has lived 22 hours and the clock is advanced from 2 p.m. to 3 p.m.. When the clock reaches 4 p.m., the tamagotchi will have lived officially 23 hours and not 24 hours according to the old time. Thus, it is possible to keep manipulating the time of a vintage Tamagotchi so that its age counter says it has lived for 50 days when actually, the tamagotchi has only lived 15 days according to its internal clock.
I've only heard of some tamagotchis on the Angelgotchi living for a ridiculously long time but also that the same source observed it wasn't consistent. Chances are if a vintage Tamagotchi lives for an abnormally long time without the clock being manipulated, then there must be something wrong with the internal clock. In that case, the internal clock may be running slow whereupon the tamagotchi will grow up and evolve much slower, or the internal clock is inconsistent which will likely cause abrupt evolution or death.