Light bulb keeps going out, but isn't burned out.
I'd try bending the hot contact in the socket out a little bit or a different bulb. If the problem persists I'd be inspecting the connections inside the junction box.


Try a different bulb (swap in a known working bulb, and swap this one out to a known working can light).
Try bending the contact out (the pin inside the socket).
Inspect the connections (remove the three screws holding the can light housing in. Pull it out of the ceiling and now you can access the junction box).


Rub the threads of new bulbs in your hair (to lubricate them) before you insert them.