My apps account synced perfectly for several hours after doing what I state below, but it's gone back to not syncing again...
Well, I got mine fixed. I went into Settings -> Applications -> Manage Applications. I choose "All" from the top then scrolled down to the one called "Email" (not Gmail). From there I told it to "Clear Data," and now both my personal gmail account and google apps work account are syncing correctly.
I don't really know why there was anything related to the "Email" app since I only use the Gmail one. I notice now that I can't even clear the data for "Email" so maybe some app I installed messed with it. Yesterday I did install the Trillian beta app, so maybe that did it.