Current investigation has shown that IRQs get switched off by "some software" in Z3 mode. It's a bit tedious to find that piece of software, as it does not seem to be anything in the driver itself.
If all else fails, I can probably make a fix in the hardware (CPLD programming) that keeps IRQs enabled all the time (i.e. make it a "write-once" register). However, I prefer to solve a problem at the cause, and not to fix the symptom.