If your inter-domain trust is down, and the eventlog reveals the following error:
There are currently no logon servers available to service the logon request. (0x51F)
Then check the following:
Check whether you can still access the DNS servers at the other side: try using the name first, then try through IP. If DNS does not work, there's an issue with your DNS.
Check whether the DNS zones for the domain are still in place. If it exists, try performing a reload from master. If this fails, you either have connection issues, or the other side has removed the required zone delegation, preventing you from retrieving the zone information.
If you can neither connect through DNS or IP, check whether the connection (VPN or WAN) to the other side still works. Also, contact the system administration on the other side to see if they haven't migrated to other DCs.