The ISR will interrupt UNLESS the task has invoked a critical section. Your symptoms seem to imply that interrupts are being blocked,
The other possibility is that you queue fills because something keeps the task from processing characters out of the queue fast enough.
Perhaps you should check the status of the write to the queue to see if that happens.
As I suggested, I would likely add a test in the ISR for the problem and just hang there, then examine the machine state to see what just happened to see what triggers it.