An addition to Box's answer:
Yes, do a search on how to fix the problem. There are a lot of creative ways to fix the problem. Some simple (Using nail polish), some difficult (Removing the switch).
The date loss is something you also have to live with. There are two solutions to fix it.
1. Use
MikelSpikel's program. Use it before switching batteries.
2. Bill Todd also made a tutorial on how to open up your Axim and change that little "back up" battery. Looks very dangerous. But it is a surefire way to fix the problem.
Here is the tutorial.
I noticed that sometimes a ROM install can make the battery door very sensitive. If you do not want to try some of the extreme method (E.g. removing the switch), I can help you reflash (Like in reinstall) you ROM (Mobile OS, in this case, Windows Mobile)
~Box, you are always mobile!