Rewind lever? You mean the wind lever.
It might not be cocking, or it might not be restraining the shutter; that is, the shutter is not staying cocked and is releasing as soon as the wind lever is returned. It's not uncommon. I've heard tell it's a bent lever in the cocking mechanism, maybe from being forced at the end of a roll. I've also heard it's a problem with the shutter itself. Either way, a CLA will fix it. Eric Hendrickson did mine. It took two tries to fix it. The camera had been "serviced" by an amateur in the past, so Eric had his hands full. He's very good.
For the 60 bucks or so it costs to do a CLA, I say send it to him. You will have a great little camera, and it will have been serviced thoroughly. If you sell it later you can get most or all of the CLA cost back.