Why don't you start by just using an indicating cube relay and a NO push button. Wire the PB and contact in parallel between the line and relay coil and return the other end of the coil to neutral. Energize, push the button and leave. If you come back to find a dropped relay, you know you had an interruption.

You could get more info by leaving the push button out and using your contacts to drive a battery powered hour meter and/or cycle counter. A N.C. contact could drive the hour meter to log the cummulative time of power off while the other N.C. (or N.O.) contact could drive the counter. If you don't need time stamping, you're done.
Joe