Why do my security lights come on after a power cut?

I have two security lights, triggered by PIR sensors.
They work fine most of the time. However, if we have an interruption to the power supply, then power is restored, they stay on permanently.
I seem to recall that the solution is to switch them off and on again (once or twice, I'm not sure), then they'll start operating as normal. However, I'm trying this at present, and it doesn't seem to be working.
Any suggestions?