Yes, you should be able to repair your strop, even some sand paper to smooth down any nicks.

I don't think anyone has asked this yet, but are you flipping your blade with the sharp edge up or down? you should be rolling your blade on the spine, with the cutting edge away from the strop. That's not always apparent. It sounds like you may be rolling your edge on the strop.
it's a steep learning curve, keep it up.