Queue full but phone doesn't ring

We have Asterisk server setup and we give out counseling every day. We have queues set up for each counselor and we are experiencing strange behavior since last friday. When user calls he is put into queue, the music on hold is playing, but the phone at the counselors desk doesn’t ring. This is not always true - some calls are normally put into queue and later, when its their turn, redirected to the counselors phone.
We were unable to extract a pattern out of this behaviour. No changes were made to the Asterisk, network or server configuration before this started to happen. We are running Asterisk 11.10.2.

The errors that are seen in the asterisk log are following:

[2015-05-13 12:15:00] WARNING[34987][C-00000002]: channel.c:4860 ast_prod: Prodding channel 'Local/[email protected];2' failed

[2015-05-13 12:15:32]     -- Launched AGI Script /var/lib/asterisk/agi-bin/dialparties.agi
[2015-05-13 12:15:32]  dialparties.agi: Starting New Dialparties.agi
[2015-05-13 12:15:32]  dialparties.agi: Caller ID name is '0013619957' number is '0013619957'
[2015-05-13 12:15:32]  dialparties.agi: Methodology of ring is  'ringall'
[2015-05-13 12:15:32]     -- dialparties.agi: Added extension 370 to extension map
[2015-05-13 12:15:32]     -- dialparties.agi: Extension 370 cf is disabled
[2015-05-13 12:15:32]     -- dialparties.agi: Extension 370 do not disturb is disabled
[2015-05-13 12:15:32]  dialparties.agi: EXTENSION_STATE: 1 (INUSE)
[2015-05-13 12:15:32]  dialparties.agi: Extension 370 has ExtensionState: 1
[2015-05-13 12:15:32]     -- dialparties.agi: Checking CW and CFB status for extension 370
[2015-05-13 12:15:32]  dialparties.agi: Extension 370 is not available to be called
[2015-05-13 12:15:32]  dialparties.agi: Extension 370 has call waiting disabled
[2015-05-13 12:15:32]     -- dialparties.agi: Filtered ARG3:
[2015-05-13 12:15:32]     -- <Local/[email protected];2>AGI Script dialparties.agi completed, returning 0

All this looks like the phone is not registered or busy but this is never true. In this state, nobody is talking on the phone, doesn’t have DND turned on and has status OK in the Asterisk Peer list.
If you need anymore information please just ask, I’ll gladly post more relavant info.