When my can lights in my kitchen, hallway and living room are turned on some of them turn off seemingly in no particular order. There is a sound that is mechanical when this happens, like a click, almost like they are to hot and there is a safety switch. I have installed 60 watt light bulbs and it still happens. What is wrong?

The thermal protectors are cutting out. I bet they are non-IC cans (Not to be in contact with insulation) and they are insulated over.
The same can happen with too large of a light bulb, but I don't think this is the case here.

Thanks! I needed some help with that one.

If you can't replace the fixture, or uncover the fixture, would fluorescent bulbs work for your application?