Jail-breaking your iPhone with firmware 3.1.3 may sometimes cause push notifications problem. In such cases, many application like email, facebook, twitter and may more which use push notifications, may not be able to provide push based services and alerts.
To fix this issue, there is a free utility called Push Doctor by anethema which can fix this problem in a blink. You need to add a repository and install push doctor via Cydia on your jail-broken iPhone / iPod Touch. Follow the instructions below to fix this issue.
Step 1: Go To Cydia > Manage > Sources > Edit > Add and type the below url in the box which you see on this screen :
click Add Source and Click Done.
Step 2: Go to search, type Push Doctor and tap search. Select and install Push Doctor.
Step 3 : Restart your iPhone.
you are done.