mine did the same thing... i used a easy one on a few of them, but some i hit with the plasma cutter then retapped... a few never did come back out so we made a braket to hold it..

Mine is just a bad gm design.. the ac dripps on them causing the rust.

 

that and they made the bolt smaller. Dumb design

 

i just went through this not too long ago. went to put longtube headers on my truck and found the back bolt on each side was broke off. passenger side one was sticking out some so PB blaster and vice grips got that one out... now the drivers side was a different story. i didnt feel like messing with it personally so i took it to a shop where they had to raise the cab off the body on that side and drill and tap that one out. $75 later it was all fixed.

 

Your message is rather old for me to respond to, however I would like to share with you or anyone reading about this problem, what I did to solve the problem.

I was unable to remove the exhaust manifold from the exhaust pipe, so I removed all bolts holding the manifold to the engine and used wooden blocks to prop the manifold far enough away from the cylinder head in order to work on the broken studs. To remove the broken studs, I used a wire feed welder and welded a half inch square nut (also known as a carriage nut) to the stud so I could use a half inch wrench to remove the broken stud from the head.

New bolts can be purchased from the GM dealership. I was told by the dealer that the new bolts are an upgrade which will eliminate the problem from happening again. I also removed the lock tite coating that comes applied to the new bolts and before installing the new bolts, I coated the threads with anti sieze.

 

Soak the bolts with PB Blaster, or better yet, Kroil, twice a day for a few days (once your truck is cool and long before you need to drive it next so it won't just evaporate off the hot headers). They will back out with minimal effort. I used vise grips on one of mine since the threads were still sticking out.