The problem is annoying, because if you have no other sync failures (such as Outlook calendar sync errors), you can't know for sure without digging into the hotsync log.
The good news is that Palm has come out with a solution to make this finally go away:
Update: Curiously, that link I had originally offered here in 2009 goes to a page that no longer offers or explains the fixpmtrace.prc file, as it used to. That's odd.
And while I found another version of the page on the site: http://kb.hpwebos.com/wps/portal/kb/na/centro/centro/bell/solutions/article/44937_en.html. Sadly, though, even that page has a failing link to that prc file.
I found all this in answering a question someone raised as a comment.
For more details, and a possible alternative solution, see my reply comment at http://www.carehart.org/blog/client/index.cfm/2009/9/7/solving_palm_pmtracedatabase_problem#c885AB116-E50B-DEA9-80CFFE5C48A7121E.
As the Palm site page discusses, you install that app onto your phone, and then run the FixPMTrace app on your device. It's important to note that it's NOT ENOUGH just to install the app onto your device. You do have to run that app from the Palm launcher (the list of apps, accessed by the "home" key, as usual) in order to have it do its magic. All it does is turn off the archive bit on a file so it stops trying to back it up.
Hope that helps someone else.
PS And before some of you jump on me for still using a Palm, :-) just know that yes I am seriously considering moving to an iPhone after several years of relative happiness with my Palm devices. I've been using a iPod Touch for a couple of years and really like that. Carrying both devices is of course a pain, so reducing it to one just makes sense.
And yes, I know about the Palm Pre. It's just that Sprint coverage in my home is really poor, and since I generally work from home, I just can't take it anymore. The Pre won't solve that (I called: they said it wouldn't likely be any better.) Since my wife has ATT and she's been happy, the forced move to ATT with the iPhone isn't a problem.
Still, I leave this Palm tip for those who may benefit.