If you take care of you Axim it will last at least 4-5 years before you have BIS or battery issues typically. There are exceptions. If you drop it, wet it, heat it freeze it or smash it you should expect less usable life. I have a 5+ yr old Cassio Cassiopea E-11 that still works and a 3 yr old Dell Axim X5 still works. Minor screen scratches are all that is wrong with them.
I would think 3-4 years. Think of the PDA kind of like an old PC. There are many older computers still working just fine, but they have limited uses,like word processing. Try downloading music or picture files using a computer thats 7 years old or better yet try playing one of the newer high powered games on one.
I had a Casio E-100 that lasted 3 years before the sound went. My Audiovox Maestro lasted 2 years before the battery stopped holding charges. My x50v shows no signs of degradation (1 year anniversary next week), knock on wood.