The sure-fire way to test and see where the problems are is to check using Outlook Web Access (OWA) and see what happens there.
If all is well with OWA, please setup a new profile on a computer that is not affected by this problem and see if the problem can be replicated. If it cannot be replicated - this sounds like an Outlook problem. If it can, then it sounds like a problem with the store.
The possibility of problems with Outlook could mean that a "Help> Office Diagnostics" could repair local Outlook problems.
Problems with Windows Mobile / iPhone can be correctd y deleting the account and setting it up again.
If the store is the problem, you will need to dismount the store and run:
eseutil /p
eseutil /d
isinteg -s servername -fix -test alltests (this needs to be run at least twice until the last line shows 0 errors and 0 fixes).
For reference:
http://www.msexchange.org/tutorials/Exchange-ISINTEG-ESEUTIL.html