Sorry to resurrect an old thread ...
I know it might be too late for the people on here who have had their problems, but I wanted to tell people about my experience with this problem, as it may save somebody a LOT of headaches in the future.
I had the "abrupt" rebooting problem as well. I thought it was bad memory as well, after reading what people did. I tried doing the "yes > /dev/null" thing, and running memtest. The problem seemed to be replicatable by running memtest, and the computer would randomly reboot.
After reseating cables again and again, resetting the SMC and PRAM, swapping sticks, etc., I happened to notice a picture on a Mac mini take-apart guide. (I was using the guide to help me take apart the Mini. It seems there is a hardware button to "reset PRAM" (according to the site, it resets BIOS). It is circled in violet in the picture. Push this button ONCE, and all your problems should be solved. I know about the keyboard shortcut, and tried it multiple times before opening up the mini (it's a pain to use the putty knife).

If anyone wants to read the guide, it's at http://hdtv.o0o.it/mini/
I know it might be too late for the people on here who have had their problems, but I wanted to tell people about my experience with this problem, as it may save somebody a LOT of headaches in the future.
I had the "abrupt" rebooting problem as well. I thought it was bad memory as well, after reading what people did. I tried doing the "yes > /dev/null" thing, and running memtest. The problem seemed to be replicatable by running memtest, and the computer would randomly reboot.
After reseating cables again and again, resetting the SMC and PRAM, swapping sticks, etc., I happened to notice a picture on a Mac mini take-apart guide. (I was using the guide to help me take apart the Mini. It seems there is a hardware button to "reset PRAM" (according to the site, it resets BIOS). It is circled in violet in the picture. Push this button ONCE, and all your problems should be solved. I know about the keyboard shortcut, and tried it multiple times before opening up the mini (it's a pain to use the putty knife).

If anyone wants to read the guide, it's at http://hdtv.o0o.it/mini/