Unless my knowledge is extremely outdated, it's never a good idea to rest any component on the OUTSIDE of an anti-static bag. You'd be better to lay it on a cardboard box.
There are two types of anti-static bag:
1. plastic with conductive paint, usually grid-lines or similar, sprayed on one side to create a Faraday cage
2. Metalized PET plastic
The conductive pattern bags are the riskiest if the paint is on the outside, but even these are usually
resistive enough to not cause problems.
The PET ones are barely conductive. For mains voltages they can be considered an insulator.
Motherboard shorts usually cause pops/sparks/smoke in my experience but I've never seen it from an anti-static bag - only from metal swarf in a badly machined motherboard tray.
ESD is usually
phenomenally high voltage (like 10,000V for all the way up to 10^12V) and almost zero current, which means antistatic bags don't have to be that conductive to be effective.
Back to the OP's problem, I'm not so sure it's related to the antistatic bag, since he mentions that the previous one was running for two days before the PSU died. I doubt he'd be running a PC on a bag for two whole days?
OP, can you confirm?
Random things to look at which haven't been mentioned yet:
- Faulty surge protector on the 4-way power strip you're using (unclean power)
- another faulty component that's triggering fuses, like worn/damaged pins on a graphics card fingers or SATA drive power connector
- the earth in your home mains wiring isn't earthed properly, or you have a faulty appliance with a high-amperage fuse on the same ring/circuit