Rebuilt calipers are generally fine, but it depends on the rebuilder.  In general, I'm not a fan of assembly line rebuilt parts...I'd rather have my own rebuilt.  That way I know the quality of the part being rebuilt.

That being said, I've rarely heard of problems with rebuilt calipers.  My experience is when it comes to assembly line rebuilt parts, carburetors are the worst, followed by alternators.  Starters and water pumps don't have nearly the reject rate from assembly line rebuilders...at least in my experience.

The problem today is most shops only remove and replace...they don't rebuild.  They don't want the legal liability for a bad rebuild job.  They can pass that off on the supplier.  Most parts suppliers don't even carry rebuild kits for calipers and wheel cylinders anymore for the same reason.

Your caliper can definitely suck air back into it...it happened to me with the '78 I owned.  It was a bad caliper seal.  Replacing the caliper with a rebuilt from NAPA cured the problem.

You don't need the engine running to bleed power brakes. 

I have 4 rebuilt autozone calipers, and master cylinder on my car.  They are stainless lined calipers.  No problem.  Are you sure the air is not coming from around the bleeder threads?  Did you bleed to other wheels to make sure everything is out of the entire system?

 Did your master run out of brake fluid at any time doing the caliper or before?

I thought about the bleeder threads leaking air.  Is there any special sealant I can put on them?  It is only the left front that has air.  I must have bled it 30 times, and air keeps coming out.  Maybe the sealant is worn off.  I bled the other 3 wheels and they have no air.  I agree the pedal always went close to the floor.  I am just nervous to drive it when I see air bubbles every day when I work on it.

Did you bleed them in the sequence that acplus notes above? Are you sure there are no cracks in the brake line itself and did you bleed the master cylinder if the fluid level got low in the master? There are easy to bleed master cylinder kits and if you keep getting air in the left front (drivers side front) I would try bleeding the master and then bleed the calipers in sequence. Good luck.

Bleeder screws bottom out to seal, if there is air getting past you may need a new screw or the caliper seat is bad...but if you like you can use a rt silicone or teflon tape to try it. Don't plug the bleeder hole though.

Do you drive the car in between?  If you do, the rotor might be wobbling enough to pulse the caliper, which will suck in air.  If not, it sure seems like a bad caliper.  We use a service that hand rebuilds each one.  Since the Auto Zone ones are so cheap, I have to assume they are done in China, with Chinese parts.  Sometimes this is OK, and sometimes there is a problem.

Larry

Any luck?

It was air getting past the bleeder threads.  I put teflon tape on the threads and finally the air stopped.  Thanks to all.