Recessed can light fixtures, called IC rated, are designed so that they can be covered with insulation without creating a fire hazard. For safety, they have a high-temperature cutoff switch that turns off the lamp if excessive heat builds up. Unfortunately, under some circumstances they may cycle on and off too frequently, which can be annoying.
To resolve the problem: First, check the information on the fixture label to make sure the bulb is an acceptable type and wattage. Second, check the fixture label to make sure the trim is compatible with the housing. The wrong trim can trap too much heat inside the fixture housing. Look for a part number on both the housing and the trim and call a supplier to confirm their compatibility. Third, if the housing allows the bulb to be adjusted up and down, move the bulb down. Fourth, the thermal protector might be defective and require replacement. This is a tough one to diagnose. If you have several lights turning on and off, the protectors are probably OK. A single problem light might well have a faulty protector. Call in a licensed electrician to fix it.
Still stumped? Try this solution that I've used several times. Build an airtight box around the problem light. You have to do it from within the attic (not a pleasant working environment!). Cut the box from 2-in. thick rigid extruded foam board, then glue and screw the joints. Caulk all seams and penetrations from either inside or outside the box. It's important to make the box airtight to keep warm air from escaping into the attic. It provides air space around the fixture to help prevent overheating, yet interior air cannot get into the attic, and your insulation is still intact.
Recessed Light Details
The label inside the can specifies the maximum light bulb size and the correct trim style. If the light is too big or the trim is the wrong style, it will cause the light to cycle off.
Before climbing into the attic, check the bulb size and bulb location inside the can, the trim style and the cut-off switch.
If blown-in insulation is making a can light cycle off too frequently, solve the problem by installing an insulated box over the light.