Snap! I also have an ABM Mini (purchased yesterday from a very nice Basschatter) with a faulty drive unit - just like yours. Mine is only starting to go, as there is no coil rub yet - but it's certainly on its way out. I'm fairly sure that incorrect cabinet tuning is the cause of the failure. My back-of-a-fag packet calculations show the cab is tuned to about 55Hz, which means the speaker will only handle about 10 watts of low E. So, driver failure has been built in and is just a matter of time unless you're using it in your bedroom.
I'll measure the cabinet tuning some time soon, and when I've managed to persuade the driver to come out (I thought it had been glued in!!), get the Thiel Small parameters, which will show us the type of driver they've used. This cab is roughly 45 litres in volume (much smaller than I was expecting), which is much too small for just about every 15 I know - but a good volume for a 12. In other words, there is no benefit in fitting a 15 in here, because a 12 will produce just as much bottom end.
Given the excessive profit margins manufacturers make on spares, I would hesitate to replace the driver with another of the same. A budget, lightweight option would be the Celestion TN neo 12" available for about £50, but you will need to fit a panel of 1/2" birch ply over the front baffle first. The 15" Celestion TN neo costs £25 more but will not actually provide any more bottom end (because of the small cabinet size). Plenty of quality 12" drivers will work in here though.
Bear in mind that the cabinet should definitely be re-tuned lower - or else the same thing will happen again. As long as you're not in a rush, I can post my results from time to time for your guidance. Incidentally, I sent an email to Ashdown yesterday late afternoon (about getting the speaker out) and they responded this morning. Very impressive!