Backup Exec 2012 Remote Agent starts and stops

Per your previous comment -

Faulting application name: beremote.exe, version: 14.0.1798.0, time stamp: 0x4f1e02d7
Faulting module name: bedsnote.dll_unloaded, version: 0.0.0.0, time stamp: 0x4f1e02bd
Exception code: 0xc0000005
Fault offset: 0x000000006a8c1801
Faulting process id: 0xe9c
Faulting application start time: 0x01d0acde1d6294d4
Faulting application path: C:\Program Files\Symantec\Backup Exec\RAWS\beremote.exe
Faulting module path: bedsnote.dll
Report Id: 6216cd95-18d1-11e5-a8f2-00155d157706

This indicates the Remote Agent is crashing on bedsnote.dll module. Does the remote server have Lotus Notes installed and used ?

And are you backing up the Lotus Notes DBs via Backup Exec ? If not, stop the remote agent services, rename bedsnote.dll to bedsnote.dll_old and try to restart the Remote Agent service and check.