The LIU eq bumped messages imply a clocking issue, bad T1 circuit, or possibly bad hardware. I don't see timing-source t1 1/1 in your configuration. "show system" will reveal the timing source. In virtually all cases of a point-to-point T1 circuit you will want one end set to timing-source internal and the other end set to timing-source t1 1/1 (or the T1 interface of the link if other than 1/1). If this is an Internet circuit from an ISP, you will almost always want the timing source to be the T1 line.
What does "show int t1 1/1" and "show int t1 1/1 perf"show? Are you seeing controlled slip seconds? If so you almost certainly have a timing-source misconfiguration.
"show int t1 1/1 perf" will give you a running history of the last day's errors and troubles on the T1 in 15-minute intervals, most recent first.
What is on the other end of the link, and how is its timing set? If your timing is set correctly with one end set to timing-source internal and the other end set to timing-source t1 1/1, I would open a ticket with the T1 carrier and have them look for errors. The last mile of T1 circuits is typically on copper wire, weather and corrosion can cause intermittent problems. Asking the carrier to troubleshoot will usually cause them to "go intrusive" and take the circuit down, so if at all possible do this during off-hours.
Seeing the configuration and show int t1 and show int t1 perf for the other end may be helpful.
Look at the timestamp in your log at 1/23/2015 4:16:30. Did you put the line in loopback there deliberately?
1/23/2015 3:25:42 PM  From:host18.104.22.168 (22.214.171.124) Fac:0 Sev:3 Msg >>> Jan 23 15:25:41 Adtran3200 INTERFACE_STATUS:t1 1/1 changed state to down
1/23/2015 3:25:43 PM  From:host126.96.36.199 (188.8.131.52) Fac:0 Sev:4 Msg >>> Jan 23 15:25:42 Adtran3200 T1:t1 1/1 Tx Yellow, Blue, Red
Based on the above statements from your log, I believe you should open a ticket with your service provider. A "Blue" alarm means your interface is receiving an "all 1's" signal from the provider which usually indicates a fault upstream from you. A "Red" alarm means that, while there is a signal, there are no frames being received. These are seen at other times as well.