Well, I already build I couple of new AM2-systems (including mine) and I don't think that it's a PSU-only issue. The only really important thing about the PSU are the amp?©re on 12V and 5V which should be at least 20A per Rail, and as long as you have the additional 4-Pin Connector (it's needed for the CPU's power) and the PSU has around 20A on the 12V rail it should be OK.

So I think it's a memory issue (especially as it takes some time till your system goes down).
The new AM2-socket is VERY picky about the memory, and in the other thread I saw that you ordered memory with only 533Mhz, which is far below what the AM2-Socket is able to use (800 Mhz, PC6400). So your issue could be an icompatibility between the board and the memory (did you take a look at the memory compatibility list for your board?), and in the worst case you also have to exchange your memory. ASUS' AM2 boards e.g. are known for having troubles with even expensive OCZ-modules, so as I build my system I went for G.Skill modules and made sure that they'll work with that board. But not everything is lost, as you could try to relax the memory-timings in the BIOS. And it's also possible that the board didn't recognize the memory and tries to use totally wrong timings, so try to change them somehow. Another possibility is that your board doesn't deliver enough voltage to your memory, modules usually have a voltage operation range (e.g. 1.9 - 2.1v for my G.Skill memory), so upping this by 0.1 or 0.2v could help too.