I agree with the first post above.. ..you need to test to see exactly where you get the issues. If, as you say, its on only the Avaya (and on ALL of the Avaya) connections, then you could start looking at the protocols being used between the systems for transferring the calls.
It could be one leg of the set up is using a different SIP version - or an out of date specification for their 'implementation' of the SIP "standard". Check compatibility between the different boxes and your VoIPswitch - if the different vendors involved have used slightly different implementations of SIP then this could be part of the issue.