I think you started down the right path as being a power issue. Given the fact the Apple tech couldn't get it to fail when he had it I suspect your issue is within your homes power not your system.
First you'll need to get a cheap [http://www.amazon.com/gp/product/B000RUL2UU/ref=pd_lpo_sbs_dp_ss_1?pf_rd_p=1944579842&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=B002Q3R7HI&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=08AQN6PY36C78VMJAE04|AC Outlet Tester] to check your outlet to see if the the outlet is correctly wired. You could also have a grounding issue if you don't have a three prong outlet. This is were you will need to call in your local electrician to fix the outlet. Even still you do need to make sure the outlets wiring is correct (don't cheat here, you need all three wires). Following the wiring back to your fuse/breaker panel make sure you have a 20Amp circuit for 120volts and ideally you should have a dedicated line for your computer and your peripheral gear. Make sure the buildings Ground circuit is in good shape. Often a grounding rod stuck into the ground or strapped to the metal water line feeding the building. Over time the wire and/or the connection point corrode (green stuff) and need to be cleaned. The rod can also have degraded and may need to be replaced or positioned in a better location to be effective. Many people put electricians grease on the exposed surfaces of the connections after wiring it up to help prevent corrosion.
So we went as far as the fuse/breaker panel and we still have problems. You may need to get a UPS to stabilize the power as your power provider maybe having problems giving you reliable power. Many of the better units have power meters which can show you how good/bad your power is.
You could ask your utility provider to test your power:
Have them put a power monitor in your house for a good week or so. They may need to service your homes power feed or replace a transformer that feeds your neighborhood.