I took quite a few photos which are all in this post, so apologies for it being graphically heavy.
Firstly, the new unit arrived, and unboxing showed it to be identical to the original, no change to voltage, current, etc. So first thing I did was connected it up as a test and checked, yep the alarm would now sound and all the X10 commands started to flow, so it appears this IS a faulty power supply that causes the alarm sounder not to trigger and the X10 commands to fail. At least I'd now determined the root cause of the fault, it wasn't the overall alarm unit.
Next, I wanted to try and see WHY the original failed and if possible make the new one last longer. One thing I'd always noted was that it ran hot, as most step-down transformers give off heat this isn't unusual, but they generally have vents or at least some way of expelling the heat. This one doesn't, the power supply is a sealed black brick, no vents or anything and when I say it ran hot, you wouldn't want to hold it in the palm of your hand long, it's that sort of heat. So my thinking is I give it some vents before I put the new one into service to help loose the heat, my thinking is most electronics prefer to run cool than hot and it might stop the failure occurring again.
This meant my favourite (ha ha) thing of all time, take something brand new that I've just paid for, take it apart and modify it! But luckily these PSUs have 4 clear screws and a simple case, so taking it apart isn't a challenge. Once opened up, split the two halves of the case carefully as one circuit board stays in one side, the other in the base as you can see from this photo with the case carefully separated:
The right is the "base" which has the main transformer and a circuit board that covers the base, along with at the top right the 2-pin mains in socket.
The left "top" holds a much smaller IC-containing board and the output wire that feeds to the alarm (4-wire). The small circuit board has a single screw in it (just visible on photo, bottom left) so take that out and the top casing comes completely clear. This was ideal, my thinking was to make air vents right along where that bulky transformer sat as that's where the heat was generated, and it was VERY snug alongside other electronics, so a good bet.
I set about the case with my dremel, and here I show my failure as a practical/mechanical/precision person, the air holes are horrible, not neat, but I sanded them down so no rough edges and I think they'll do the job.
As you can see they aren't neat, but should allow a bit of heat to escape. Putting it all back together and it looks like the vents are in the right place, right over the transformer.
Putting it all back together, power on and it all worked fine!
(Note for later, when the batteries are low, the green battery light stays on! I thought the power supply had blown somewhere in the process as the green light stayed on. Seems the green light not only shows it's running on batteries, but also that the batteries are low!)
Next, I decided to properly pull apart the old supply, as I'd like to find what failed and possibly fix it, so in future I have a way of repairing these things with just a few parts.
Below are a load of photos of the teardown, I've not yet had time to investigate all the parts but will do very shortly and probably try a trial and error of replacing parts until I discover the failed unit. However as you'll see there are quite a few scorch marks on components, so I'll be starting work there, which is also where I believe the mains part of the circuit resides, hence this bit will be more susceptible to mains spikes, etc, (which is what Marmitek/Haibrain state as the issue when the PSU fails, it's a mains spike)
After removing the transformer, some scorching of the main board was clear, I'm now suspecting this is where the issue is.