The below is the basic first level troubleshooting needs to be done in the BB device client side.
1. Check the signal strength.
2. Checking the wireless network connection setting
If the signal is good, there is no need to check the wireless network connection setting, but when the signal is down make sure the wireless network options are set. Check in Menu --> Options --> Mobile network options --> Make sure data services is on (mobile network and network selection mode is set appropriately)
3. Check the availability of the PIN Number in the device. Device --> option --> status --> will find 8 digit alphanumeric PIN Number. If you don’t find the pin number, try to register the device by going to Device --> option --> advanced options --> Host routing table --> press menu key and choose register. This will register your device in the BB RIM and the new unique PIN number will be generated, still if you have the issue in getting the PIN Number, then the problem is with the device and needs to be checked with the vendor.
4. Can check the mail flow from the BB device itself to the same connected user account or can send test PIN message to the same device account.
5. If you're having mail or messaging issues, or any other BlackBerry performance problems, you should resend your device's service books.
6. We can use the Blackberry device manager for synchronizing the BB device with the server i.e., outlook email client.
If the above are fine, then troubleshooting needs to be done at the BES server side like BESAdmin account permission, mailbox quota check, BB device last contact time, BB detailed event logs and goes on. Probably I will document an article on that front in the near future.
Hope the above information is useful.