Dartin for Divorce

Could be a vibrational thing, where it settles in to a "connection" state through spring action of the metals. After you start it & shake it around a bit, the spring relaxes (or gets rattled) and doesn't want to make contact any more. Back in the 1980s Ford created their "Wiggle Test", which involved wiggling wires to find intermittent problems. Maybe disconnect the relay, put a volt meter on it (or test light), and have the kids start wiggling wires for you. Do it in a controlled manner, of course. When you meter goes berserk (or the light goes out), find out what was just messed with & go from there. A test light might allow you to do the test by yourself.