I need to fix a recess light in my kitchen?
Turn off the breaker to this circuit.
Near the bottom of the can light there are three screws. Remove them and the entire inner tin-can should pull down out of the ceiling. You can now rescue that screw and deal with whatever the problem is. This also provides you access to the junction box that is part of the lamp; where its connections are that you need to inspect. 

A can light that seems to turn itself on and off either has too high of wattage bulb in it, causing the over-temp sensor to trip. Or the over temp switch has failed and needs to be replaced.

I am at a loss as to why one would burn out bulbs faster than others, unless it is somehow subject to more vibration. I'd check it against the others with a meter to make sure everything was kosher.