Do you have a thread dump from the application server during the time you observe this issue? That should indicate what the MDBs are doing (if anything).
I don't have thread dump. I observe server via jconsole. I'll try obtain thread dump.
Sorry for late response. Thread dump helped us find the issue!
We found out that multiple threads (MDB pool instances) ended up in deadlock in one of ours business logic methods.
For thread dump we used jstack.