My Nikon D60 let me down?

I use a Nikon D60 with a SC28 sync cord connected to a SB800 Flash. Last night during a very heavy use period, the flash seemed to stop communicating with the D60. The flash would fire sporadically then fine for awhile, then act up again. My question is which piece should hit the dumpster, the sync cord (which I think is the culprit), or the SB800 (which may be the problem) or God forbid, the D60.

It sounds like weakened batteries in the flash, camera, or both (remember, it was following a period of heavy use, a point to
which you admitted).

Try taking some photos today with the same gear, and see how things go. Then try fresh batteries.

"very heavy use period" - that's the clue - if you were at 1/4 power or more, you'd be using battery power heavily, hence the recycle time was getting longer as the battery power went down.

Heavy use of the flash could also trip up the thermal protection mechanism in the flash. You must realize that the flash dumps a huge amount of energy in to the flash tube. Did the flash feel warm when things went wonky? Might be a clue.

Charge up all batteries and try the combination again. If all is ok, then you either had a battery problem or an overheating problem. Your manual discusses the overheating issue.