I had the same problem - what I did to fix it was first deleted the MobileMe account that wasn't working. Then, before I added it again, made sure that the Settings, "Fetch New Data" was set to "Push." I then added the MobileMe account and turned on pushing for mail, calendar, contacts, and bookmarks.
When you sync to iTunes, make sure that the checkbox to sync the Mail Accounts is off.
Hopefully this works for you too.