I was stumped by this one.
I was planning on replacing a freewheel for a friend's bike because it would not engage. I tried lubricating it and spinning forwards or backwards in all sorts of gear combinations; nothing seemed to work. However, when I removed the freewheel (6 speed Suntour four prong type), I noticed that it engaged perfectly in my hand. So, I reinstalled it on the bike, and it's engaged perfectly ever since then.
Is there any reason to believe the freewheel might spontaneously stop engaging again? It wasn't screwed on unbearably tight to begin with, nor did it appear to be cross threaded or mounted incorrectly.