I have an old early 80's snowblower, the recoil wasn't returning so I pulled it apart and cleaned it all out and got it working. I used it to clear the driveway, stopped and started it a couple times that night, and put it away running. We got snow again today, I went out to start it, and it didn't start on the first pull, but it turned over fine. When I pulled the second time there is no tension on the recoil rope, it returns fine, but there it is not turning over the motor. What could have changed from the first pull to the second??

There is a ratchett mechanism inside that recoil that allow the spocket to slip backwrads around the engine drive shaft but engage when you pull the other direction. That ratchett and springs are gummed up or the springs broke. Disassemble and start inspecting. I'd simply buy a new recoil assembly to save time and trouble, they are about $20.