When I need to do a quick test to verify BE is sending SNMP traps, I use an SNMP capture utility called SNMP Trap Watcher (from BTT as freeware http://www.bttsoftware.co.uk/snmptrap.html)
Basically on my media server I have made sure that the SNMP Trap Servcie is disabled, that the SNMP Service is started and that it is configured with a public trap destination of the IP address of the media server itself (which would usually need to be set to the IP address of the system running your SNMP tool) Note I restart the SNMP Service if I have changed the trap destination IP addresses
I have then started SNMP Trap Watcher on the media server
I then switched to the Backup Exec 2012 console and used the yellow BE button top left to select Configuration and Settings --> Alert Notifications --> Alert Categories
I then picked an alert of interest and made sure Send SNMP notification was enabled. I used the Job Start alert as a very easy one to test with.
When I did this just now and started a job - TrapWatcher did capture a Backup Exec job start message. As such BE 2012 is able to send SNMP alerts. Environmental note - I was using 2012 on Windows 2003 and I had no firewalls or other security software blocking SNMP traffic.
You might be able to use a similar test to confirm the SNMP operations of BE which might then leave the issue as something within your trap monitoring product
