OK, so the speed dial works, you said "it connects the call and drops it within 8 seconds", so the speed dial code itself works from your statement. I assume you tried just dialing the speed dial code from your phone to verify? And I assume the ACD path portion works fine?
It sound like the problem is taking an incoming SIP call and redirecting it back out as another SIP call unsupervised? There are numerous reasons this could occur, COR, COS, SIP Peer Profile settings, incorrect outbound CallerID, etc. Does a supervised transfer work? Meaning, if you call your DID number, answer it, then try to transfer it to another number or speed call entry, does the transfer start successfully, can you communicate with the far-end, press Trans/Conf again and make a 3-way call, disconnect and the call stays up?
How are calls triggered to go to the cell phone, when everyone is logged out of the ACD path, when the system is in Night service, via a Nupoint Call Director mailbox, or some other means?
Often times the best way to troubleshoot this is to make test calls and analyse the SIP messaging to see where the call is being disconnected and why...