First, check the voltage at the fixture.
You might screw in one of those plug adapters
to make it easier to put in the volt meter
probes. Utilities are supposed to deliver
120 volts give or take 5% to your service
entrance. If this is the only bulb giving
you trouble, the problem could be in the
neutral wire to it. Look at the voltage with
various other loads in the area on and off.
If you ever get over 126 volts, chances are
what you have is some place where this
circuit shares a neutral with a circuit on
the other hot. Current codes don't allow
that, for this very reason.

Also, check for any voltage at all between
the neutral and ground at the suspect socket.
If you find more than a couple volts, that's
the problem. You'll probably need a good
electrician to figure it out and fix it.
The solution is to pull in a proper neutral
for every circuit.

The other possibility is that your utility
is giving you too high a voltage. But in
that case, you'd see lots of bulbs with the
same problem, as would your neighbors.

-- J.S.

Theresa,
Several things come to mind.

1) Before doing all the checking suggested in the previous post check this: Are you using the proper wattage? Inside the can is a label that will tell you the maximum wattage. If you exceed this you will shorten the life of the bulb and are risking a fire.

There may be several wattages listed. It depends on the insert. If in doubt, try a lower watt bulb.

2) Another possibility is that you are using halogen bulbs and the fixture is getting too hot. When cans get too hot, they shut off until they cool down. You may be seeing it at this shut-down phase.

3) According to your figures, you get about 7 weeks per bulb. At 24 hours/day thats around 1200 hours. Many incadescent bulbs are good for 700-1000 or so hours. Try a different brand, ie) a long-life bulb rated for 2000 or more hours.