If you boot up into a fresh Workbench installation and leave the Amiga alone for longer than five minutes, does it crash? Or does it only crash when running software?
If you bump or bash the desk from underneath, does it cause the Amiga to crash? If so, it's possible the accelerator's expansion connector isn't clamping on properly. If this is the case, you can carefully bend all of the teeth inwards towards each other slightly about 1mm so it bites down on the A1200 edge better to form a more stable connection.
Also, if you remove your hard drive and boot up Workbench from a floppy disk and try the same programs, does it still crash? Sometimes a few extra devices in an A1200 can draw too much power for the PSU to handle, even the A500 one. I'd recommend replacing the hard drive with a cheap IDE-CF adapter and a 4-8GB Compact Flash card, which will boot faster and use less power than the hard drive.
It's very possible that your Amiga has some software or patches installed that are conflicting with the accelerator, so booting into a freshly installed Workbench should help eliminate that possibility. If you want to try this, make a new drawer in your boot partition called "WorkbenchOLD" or something and move the entire contents of the partition (except the new drawer) into this drawer, then you can install Workbench without losing your old setup, just do the same thing again and swap the installations around when you need to. If you keep it on the same partition, moving everything should be quick to instantaneous.
