Nick, I realize that this sounds obvious, but some part of the clutch is getting stuck and you are the one who is looking at it. The starting part of the clutch is a control lever, a cable, an operating lever and aclutch disk. If any of these parts are getting stuck, they will look and feel different than when they are not stuck.
If the centrifugal clutch is stuck, it will feel like the starter clutch is stuck except that the operating lever will not move because the clutch is being held on from the inside.
The only solution is to clean, lube and/or replace whatever is sticking. Make sure none of the lube gets on the clutch surfaces.