Blinking recessed light in my kitchen after its been on for a while.

Power company is playing games with you.

Try changing the bulb to a lesser wattage. Some recessed lights have a heat activated sensor. Could also be a connection problem.

If it's florescent it could be he ballast box going out.

If the present bulb is too high a wattage recommended by the fixture, and you switch it out with a lower wattage bulb, you may find that it is not sufficient light. If so, then buy a new LED light bulb. It will be higher priced initially than an incandescent bulb, but will last years, and there is no heat issue to be concerned about.

You could also try screwing in another light bulb. If you find that the blinking still occurs, then you know the source of the problem is the fixture/connection and not the bulb.

How old is the fixture?

O.K. , that narrows it down somewhat, as you now know that the problem

wasn't the bulb.I am wondering if it might be a loose connection somewhere closer to the lightswitch on the wall that controls this light turning it on and off.

Turn off the main power source first to this wall switch.

Then take off the light switch cover and give a visual check if there are any wire ends that look frayed or pinched. If there are, then do not turn on the main power source to this switch again unit the wires are properly repaired.

Then feel each screw to check and make sure that they are all screwed in tightly and have not come loose. Is the silver box still anchored tightly or is it loose? Re-tighten any that may need it.

Put the lightswitch cover plate back on the wall, turn on the main power.

Try the light again, with the new LED bulb, and see what happens.