The outlook calendar and reminders are always headache to IT support staff, since it is extensively used by the top management of any company and gets limited time to resolve it. Here is one such problem I have come across recently and the simple resolution.
You might have experienced the reminder pop up issue with the users who are running Outlook 2010, Service pack 1(mostly after you upgrade the outlook 2010 with service pack 1). Whereas the user gets his reminder pop up when he uses the Webmail (Outlook Web Access).
This issue is acknowledged by MS long back, however the hotfix intended for this issue include fixes for many other reported issues. Hence it becomes difficult to point down to the article when you search for it. This issue is addressed in the Microsoft Knowledge Base article number(s) 2584053.
Request for the hotfix from the below link,
Download the hotfix mentioned in the above link and verify the reminder functionality again. It should work like a charm!
If it did fix the issue for you, I would recomend you to deploy this on all Outlook 2010 SP1 machine to kill the issue before it pops up !