Dear Expert,

Can I patch/repair a dime-size hole in the wall of the combustion chamber of my wall-hung furnace? This is a natural gas, NON forced air ambient heating unit for our basement and has always worked well. The small hole prevents the pilot light from staying lit. Can this be repaired? Please advise.

Because of the high heat involved, its not a good idea to patch something like that since there is carbon monoxide involved. Are you saying, if you block the hole somehow the pilot stays on but when you unplug the patch, it goes out? Usually if a pilot will not stay lit, it's the thermocouple that's bad.

Dime sized huh? Do you know what a molly bolt is? If not you can ask at a hardware store. It folds closed to push into the hole and then pops open (like a T) so it can't come back out easily. If you get the proper size molly of the proper length to use with a washer to cover the hole (it has to be long enough so it can open when set in place with a washer on it (taking in the thickness of the metal wall). You can put the washer on the screw, then the folding molly part, fold it up and put it on the hole. Then pull back on the screw part to hold the molly against the wall inside, and tighten the screw (it can be tricky). You can also ask at the hardware store if they have heat resistant sealer to put on the washer and screw head for a real seal.
The thermocouple is a heat sensing rod that's put in the pilot flame to detect it. If it doesn't detect a flame, or if it goes bad, the main heat valve will not open and the pilot will often go out.

The thing is, if the hole is preventing the pilot from staying lit, there has to be a sensor involved. And if its not forced air, it shouldn't be an air pressure sensor. Is there any fan at all in the unit?

Not a good idea. You have one hole so there are probably several more ready to open up if this was caused by age. No HVAC repair shop would do a patch because it is not safe. You can try any DIY project you want but it could be dangerous to you and any one else in the area. If I had to patch to get me by I'd MIG weld a piece of steel the same gauge as your heat exchanger.

Replacement of the entire exchanger is really the best alternative. If the hole is from rust, patching is only temporary (maybe to get you through the winter) although there could be other holes you don't see. I suppose if the hole were a clean puncture, a patch could last for years and cost about 1/100th as much to fix.