Just to comment on this question since I don't have any version of the program running 24/7 (and don't really see a need to run it that way to question its stability).
Those who do use this program should remember that it is a computer program and unless they have clean and stable dedicated computers to run it on, the program could randomly crash either due to operator error or flaky hardware or some other software or just plain timing/communication issue (this not necessarily related to any programming side of it since most bugs do get reported and fixed as soon as they occur). AHMI users are the ones creating applications so they should always try to look for any possible mistakes they might have made. Windows itself might randomly crash, "for no reason" as some would say.
If the program is capable of running for 1 hour it should be able to run for 1 or 10 years as well.
There is always room for improvement but I think that this program is extremely good and stable as it is. If version 3.52 is not good enough for someone then just try another version (it's free anyway), or if you do find a bug in any of the latest releases then just report it. Just generalizing and not referring to Sprungmokey's post at all, since he suggested that this particular version 3.52 works just fine.
De gustibus non est disputandum --> it refers to a taste but, to quote Wikipedia article
http://en.wikipedia.org/wiki/De_gustibus_non_est_disputandum , "the implication is that everyone's personal preferences are merely subjective opinions that cannot be "right" or "wrong," so they should never be argued about as if they were" (unless one can provide facts to support it, which in the case of AHMI stability, and from a few responses received, plays in her favor).
English is not my native language, so if you do find something stated above as unclear then just let me know.