I was having this same problem. The widget wouldn't update at the interval I had it set to. Also, I was getting duplicate notifications of mentions even after I read them. Installed the Android Twitter client and have been happy ever since.

 

IMO, there are MUCH better Twitter clients out there than Peep, and I'd recommend you using a different one for the sake of userability/customization.

Twitdroid, Seesmic, Twicca are all great ones to give a shot.