My first saw was an 041 Super, a performer in its day...
After a while, it started behaving as described and actually sucked in the gasket above the heat insulating block (below carb). Replaced the gasket and had the whole thing happen again.
I figured there had to be a problem with a mating surface somewhere between the bottom of the carb, what I recall as a plastic plate that formed the bottom of the clean air volume, and the heat insulating block. Sure enough, the top of the insulating block was not flat, it was low between the carb mounting studs.
To fix it, I think I put a large single-cut mill bastard file on a firm surface and moved the block over the file, being careful to exert even force across the block and to clean the file frequently. The block is about an inch thick and I think it was something like Bakelite (but tougher) with two aluminum sleeves molded in for the studs to pass through.
With the heat block now flat and all new gaskets, that problem was over. This was back in about 1979, so I hope I'm remembering correctly. Anyway, I hope you can get that 041 S running well.
The various 041 versions were pretty good saws, but they certainly were shaky compared to later saws, so keep an eye out for screws coming loose. Maybe even use some Loktite. I always carried some spare screws on the fireline.