1) You say they're basement outlets. Is there a chance that those outlets have gotten wet in the past? It may be that the connections the wire makes with the outlet are corroded.

If you know which circuit breaker is used for that outlet, you can turn it off, remove the outlet trim cover, and remove 2 screws that hold the outlet in the box. You can then check the wiring and see if there's indications of corrosion or overheating. The outlets are very easy to replace - they're less than $1 and you only need a screwdriver (and maybe some pliers to bend the wire around the screws). If the wires are just pushed into the back of the outlet, then that may explain the problem too - connections like that often aren't very good (there isn't tight enough contact to the wire). Such outlets are common.

2) The treadmill probably doesn't take very much power (maybe 1/2 HP - about 400 Watts = 3.5 Amps. The circuit breaker is probably rated at 15 or 20 Amps). Try using a different outlet (but use a good extension cord if you need one). If you get the same result on a different outlet then it might indicate something is wrong with the treadmill (a short somewhere?). Or it might indicate that the problem is more common than you suspect.

3) I rented a place that had really crappy circuit breakers once. The breakers wouldn't trip - the contact would simply get corroded over time and the breaker would overheat. It had similar symptoms to your description - the circut would die and then come back to life after a while. Or it wouldn't come back at all. I ended up replacing a couple of the breakers before I moved out. They were ~ $25 or so as they were an off-brand that was hard to find. (An upstairs neighbor had a fire in his place - I wondered whether it was due to faulty circuit breakers (especially after seeing evidence of arcing by the main breaker for the building in the laundry room. The management did replace the bad main breaker when I informed them about the problem.).

Try cycling the breaker for the outlet. If it behaves better after that, you might want to have an electrician come and look at it to make sure it's not failing. An electrician is much cheaper than having to replace your home.


Now that I've scared you, it's my guess that it's the outlet or the connections to the outlet, but you probably should have someone look at it to make sure that it's not something serious.

Luck!

Cheers,
Scott.