I had two, double-bulb motion detector lights installed about 10-11
years ago; I don't know their brand. They're the kind that you can make
stay on by turning them on [via the lightswitch inside], letting them
warm up for a few seconds, and then turning the lightswitch off and
right back on. If you don't do that, but just turn it on once, they'll
remain off unless the motion detector senses something.

Okay, here's the problem: The motion detection is working fine on both
of them, but the 'staying on' thing is no longer working.

I have no idea what the problem is, but it seems logical [to me] that
it's NOT a sensor problem. If that's correct...what is the problem?
Any input will be greatly appreciated!