I had three canned ceiling lights (75W fixtures) that I recently replaced with LED recessed lights. They are all on the same switch. The first indication of trouble was that they could not be dimmed with either a conventional dimmer or an LED dimmer. They would not dim, but would flicker when set low, then go out all at once. Then one of the three began shutting off shortly after being turned on. Now the third light never comes on.

I am inclined to think there are too many lights on the same circuit. Any ideas as to what might be the problem or what could be done to fix it?