When you cut the strop it does degrade the blade. Also, stropping technique makes a difference. If you have dulled the edge you may have to touch it up.
Stropping sound should be even if you are doing the same things in both directions. If not, take a close look at pressure, toe leading angle etc. Something you are doing is different.
I recommend you touch up the razor on a hone or a balsawood strop with CrOx and then strop again. Also, sand out any cuts on your strop so the blade doesn't catch the leather.

I have to add -when I was starting out a few months ago, I found that my shaves would be inconsistent. I'd get one or two good ones and then one horrible one. Don't worry. As you gain more shaves under your belt, your shaves will become more consistent.

Good luck and keep us posted on your progress!