Over the last couple weeks, I have lost my idle mix screw twice.  I have been lucky  enough to find it both times.

I started checking the situation over today and found that there are no threads in the carb body. The threads on the screw are fine.

Anybody have any suggestions about repairing this? It's annoying having the screw fall out.  Lets in too much air and backfires like crazy.
Runs perfectly fine with the hole covered without the screw in it.

Steve,
Are you certain there are no threads? Not saying you are telling stories because you're there and I'm not, but that screw had to get wrenched in there pretty good to completely strip out the carb threads?  Do you have gorilla hands like my dad?

If in fact there are no threads, I'm not positive what to say. Never tried to repair a carb like that.  JB Weld can do some really cool things if you have a tap the right thread size to rethread it, but that can get goop in the air/mix hole and create worse problems.

Now, I had an issue on a lawnmower that had a screw that would not stay where I set it, and what I did was set it where I needed it and then squirt some oil resistant silicone in the hole behind it making sure to get it all the way to the screw.  So far, so good.  Maybe try that first?

NOTE:  Batman beat me to it.  Great minds think alike  

I'd worry about some of the teflon tape tearing off and potentially getting pushed down somewhere where it doesn't belong. Not that it can't be cleaned out, but why chance it.  I like the RTV idea.

Yeah, you definitely got a unique one there. Not that it makes a difference, but if you weren't the first owner maybe the PO did something to booger it up.  If not and you opened up the plug and have always been careful with it, maybe you got a carb that was cast with a flaw and they didn't care because they were plugging it and thought it would never matter.

I would suggest only putting the first bit of RTV on the screw where you think it will contact the threads in the carb body. If you try to goop any RTV in the carb body first you risk pushing some of the RTV into the air/mix hole down in the carb and you don't want that.  I think even without any RTV on the threads it would hold with a glob packed in behind the screw, but I like your idea of trying to put a little on the threads.

One other thought would be to source a small rubber o-ring that is a hair larger than the one that is currently on the air/mix screw that would hold a bit more pressure on the screw IF you can wedge it in there, but there is already not much room and the stock o-ring fits in there kinda snug so you may end up making matters worse.  Probably good to stick with the RTV.

FWIW, yours should look like this, with the o-ring, washer, spring, screw.

I'd probably try to create threads. Tap and die, if both sides are shot. The cutting raises the brass between the grooves a tiny bit. If you can just get it to engage, then you can set it, and use some threadlock. After the adjustment, medium, not the red stuff.

OK...Here's what happened with the idle screw.

The RTV that I spread thinly around the perimeter of the hole where the threads were worked like a charm.  When I put the screw in, it was a little tight but bit in well and turned right in like it had regular threads.

After turning the screw all the way in, I removed the screw to see what happened inside.  There were a few pieces of RTV that it had cut loose on its way in. I had to pull them with a very small set of tweasers to get them out so they wouldn't get sucked down into the passages.

It seems to be running well.  The screw is held well around the sides by the RTV and doesn't try to back out.  I am still playing with the mix to get it just right but wanted to let everyone know the outcome.  $3 for some RTV and a little time is much better than buying another carb.