Just to let you know, and personally I don't really mind, but some of the guys on here will get pissed at you if you start too many threads about the same thing. Just FYI.
If dirt is getting into your engine, then yea, it sure could cause problems. Little bits of dust will get all into the piston and sleeve area and basically grind away the surface. These engines don't have O rings or anything, they rely on bare metal to bare metal contact to keep pressure in the chamber. They are very high performance little motors and this metal to metal contact is the reason they don't last very long. It wears out. You can see how little bits of dust and dirt could ruin that seal.
The oil on the air filter helps catch the tiny little particles that would otherwise escape into the carburator.
If this is what the problem is, then there's really only two things you can do about it. Assuming there's no other damage in the engine, and the sleeve and piston still look to be in good shape, you can get the sleeve pinched. There's a guy that calls himself OS Rocket (you can find him on eBay) that does the best work. He doesn't just use a pinch clamp, he uses some contraption that also heats the thing or something, so that it's even tighter when it cools. It's like $15 or somthing to get it done.
The other option is to simply replace the piston and sleeve. Depending on the engine this may or may not be worth it.
Of course, the sleeve might be fine, and you could just have an air leak somewhere. When the engine heats up the metal expands and if there's something not sealed perfectly, like the backplate or the cooling head, air could start leaking and you can lose compression. Usually you can see when the thing has an air leak because fuel will leak out or dust will collect a lot where it's leaking - but this isn't always the case.