Can lights often have thermal hi temp cut off switches in them. What you describe is a situation I have seen before....too large a wattage bulb, and/or insulation too close on a non-IC fixture. The can heats up, the switch turns off, then it cools and light comes on again for a while.
Can you tell us what the label on your can says about bulbs, and what bulb you have in there.?
Is your can rated as type IC, and is there insulation on top of it?