I have an extended ACL applied inbound to my two external interfaces (two separate ISP's using BGP). Within the ACL, I have an ACE for allowing established TCP connections, i.e. "access-list 100 permit tcp any any established ".
Will this cause a problem if a SYN packet enters one interface of the border router, the SYN ACK packet leaves the other external router interface and the ACK packet returns on the original interface?
IMHO, reverse path checking is causing your trouble.
As you mentioned, the packets sent by remote users are coming through one serial interface, while the servers are sending packets back which are sent from your router through the second serial interface.
In that case, when reverse path checking checks the incoming packet, it finds the source IP address coming from a wromg direction (route to the source address points to the second interface) and drops it.
When only one serial interface is active, the problem "disapears", as reverse path checking result is OK.
It's strange you are saying you see the SYN packets on your FW, I would expect them not to pass at all.
So I'd suggest to disable reverse path checking and observe if that helps.