Replacing recessed cans difficulty?

[bazookaman]

We have two recessed lights in our kitchen. One of them is out. Sometimes it comes back on. Sometimes not. The other one works fine. Both are on the same switch. My first thought was the light bulb. But that didn't fix it. You can tap it with a broom handle and it comes back on for a little, then goes out again. So i thought perhaps a loose wire. I took out the light and checked the connections and everything seemed tight. So now I'm thinking I just need to replace the whole thing. They are original to the house so around 16 years old.