I got home a few days ago after being gone for a couple months and I noticed one of the lights (CFL) in my kitchen isn't working late at night. If I try to turn it on after around 10:30 PM it almost certainly won't turn on. I just tried it around 10:45 PM and it turned on at about half brightness for about half a second and then went off. It works fine earlier in the evening, and it's been doing this for the past 4 nights (since I got home). What could be causing this? I don't think it's the temperature, it's about 74f in my house right now (11PM) and it didn't get hotter than 80f today.
First you need to identify if the problem is in the bulb or the fixture. Swap the bulb to another fixture and place a different bulb in this fixture. If the bulb is the problem, replace it.
If the fixture is the problem, I'd start by checking the voltage in the fixture when there's a problem. Then check the voltage at the switch. There could be an arcing wire resulting in the low voltage, and creating a fire risk that you'll want to resolve quickly.
It's also possible that a thermal protection switch inside the fixture is activating and starting to cut power to the light. If that's the issue, and there isn't a problem like insulation covering the fixture, then replacing the fixture is likely the easiest fix.