If it ain't a 8830 or 8300 running orignal release software, a good reset will likely clear it up. Remove the battery for 30 seconds and replace. If you have already tried that, make sure reminders are set on the appointments.
I had the same issue with my wife's 8300. I found the solution on another website, but I did post the link somewhere on this forum but I can't find it now.
Search google for "blackberry reminders/alerts" and you will find a link to get the patch that fixes this problem. Once the patch was applied she had no more issues with alerts.
I hope you find it, I will try one more time to locate the link for you.