Here is what Motorola Level 1 Support told me. In a nutshell, they suggested using Gmail's Mail Fetcher, or resetting the phone to factory settings.
Gabriela A: Hi, my name is Gabriela A. How may I help you?
Ken Hammond: I have a Droid that keeps losing all of my email and settings.
Gabriela A: I am sorry to hear about that problem.
Ken Hammond: i see from the support forums that this is a common problem.
Gabriela A: Is this problem happening on a Gmail account or a Corporate account?
Ken Hammond: I have five personal POP3 accounts.
Gabriela A: Have you tried removing the battery for 5-10 seconds and then power the phone back on?
Ken Hammond: I have not, but it was also not syncing with the email servers. To resolve this I did a full power-down and power-up. But I did not remove the battery.
Gabriela A: Ok. One moment, please.
Gabriela A: You can try using the Gmail's mail fetcher, Gmail's Mail Fetcher can download messages from up to five other email accounts, centralizing all your email in Gmail.
Gabriela A: If you want, I can send you an e-mail with all the instructions on how to setup Gmail's Mail Fetcher on your Droid.
Ken Hammond: Is that set up in Gmail? I'd prefer not to have copies of all my messages on the Gmail server, but if that is the only option...
Gabriela A: You can try with that. Another option will be to reset the phone back to default.
Gabriela A: Factory Data Reset is a tool used to remove everything that was imported, added or installed on the device.
WARNING: When using this feature; everything is deleted.
Nothing stored on the MicroSD will be affected.
To Perform a Reset
1. Open the Applications Tray. (arrow pointing up located in the middle at the bottom of the display screen)
2. Touch Settings
3. Touch Privacy
4. Touch Factory data reset
5. Touch Reset Phone
6. Touch Erase Everything
Ken Hammond: That would erase all installed apps and settings, correct? What would prevent it from happening again?
Gabriela A: Actually, we cannot guarantee that. But by resetting the phone, the memory is also refreshed.
Ken Hammond: I would be willing to do that once if it would resolve the problem, but installing everything again is no fun.
Gabriela A: I understand that, sir. We apologize for the inconvenience, but these are the troubleshooting steps.
Ken Hammond: Is support working on this problem? If so, when is a fix expected?
Gabriela A: We do not have any reported issue about this problem, sir. If you prefer, I can escalate this issue to our Level 2 who will contact you as soon as possible with all the information you may need. Is that right for you?
Ken Hammond: Yes, let's escalate. This is a very common and serious problem, as you can see here:
http://www.droidforums.net/forum/tech-issues-bug-reports-suggestions/6645-droid-spontaenously-wipes-e-mail-configuration-8.html
Gabriela A: Ok. I will forward this information to our Level 2 support team. They will contact you as soon as possible.
Ken Hammond: Thank you.
Gabriela A: You're welcome. If you need any more information get in touch. Thanks from Motorola, bye!