Losing Apps when syncing with 2nd computer
I've been fighting with these types of issues for about 2 months now. I called Apple (again) today to specifically talk about this issue. Here is what they told me. I won't know for sure if it works until tomorrow.
I sync Outlook contacts & calendar at work (2nd computer) and everything else at home (1st computer). Lately it has been deleting most of my apps on my phone.
The iPhone only "syncronizes" with Outlook, trading latest info between phone and computer. All others (music, podcasts, apps) only download from computer to the phone. The good thing is that you can't delete music or an app permanently off your computer accidently by deleting it from your phone.
You must have your iTunes on the 2nd (work) computer setup up to only sync Outlook and Apps. All the others (music, videos, etc.) must be unchecked. Also, in order not to lose your music after syncing with the 2nd computer you must uncheck the "Automatically sync when this iPhone is connected" checkbox on the Summary page in iTunes; check the "Manually Manage Music and Videos" checkbox on the Summary page in iTunes; on Info page in iTunes Check "Sync Contacts with Outlook" and "Sync Calendar with Outlook" checkboxes ONLY on the second (work) computer (not on #1 computer at home); Check "Sync Applications"; uncheck sync music, videos, podcasts, etc.
To prevent losing apps:
After all that is done, on 2nd computer iTunes Right-click DeviceName (name of your iPhone in left side of iTunes under Devices) and click Transfer Purchases. Then you can sync. We'll have to do this two set process every time we buy a new application.
PS - I think it is a good idea to do this with your primary computer too after buying an app on the phone just to make sure it gets backed up on the computer.