When turned on, the lights seem ok for a few minutes, but then they start to slowly blink on and off. Each blink lasts between 10 - 30 seconds. So, a light will be on for 10 seconds, off for 20 seconds, on for 15 seconds, off again for 30 seconds, etc.
The length of time between blinks is variable and the lights are not in sync with each other. The effect is like a slow-motion disco.
The lights were previously on a dimmer. It was suggested to me that the dimmer switch might be at fault, so I replaced it with a normal switch. The problem has not gone away. When I had the dimmer, I could set the dimmer at half power and the problem would not occur (though I would be stuck with constant mood lighting).
I had an electrician come out, inspect the problem, and give up. He suspected heat-related issues, but he checked the temperature and said it seemed ok.
Based on suggestions in the comments, I have replaced one of the CFLs with a 12 watt LEDs (this kind).
Unlike the CFL bulbs, the LED bulb has a noticeable flickering when it is on. In addition, it also still exhibits the "blinking" effect described above. In other words, the problem persists.
I could replace the other two CFL bulbs, if somebody thinks that one of the other bulbs may be causing issues with its siblings. I don't know what I am doing, but this seems unlikely to me, so I have started with replacing only a single bulb.
Would using incandescent bulbs make a difference?