I think amiga1260 hit the nail on the head there. It is probably power consumption. The PSU on a standard A1200 is only 23w, whereas the standard A500 is 60w. Try using your A500 Power Supply on the A1200. If it works, get yourself on ebay and buy a 60w A500 Power Supply.
I run my A1200 on an A500 psu as I only have a RAM card and HDD so I don't need a "Goliath" type PSU, just something more substantial than the standard A1200 one. If you have/are intending to get an accelerator for your A1200, you should consider a "Goliath" PSU (normally found on ebay).
