I don't find a difference in shave quality when I shave on consecutive days, or when I take a few days off. There may be a difference in the number of passes I need to get to bbs, but thats about it. Maybe Your shave was more comfortable because your technique is improving.
Let us know what specific model strop you have. It does sound strange. The leather side to a strop should be very smooth feeling - not like suede.
No, in all these things we are more than conquerors through him who loved us. For I am sure that neither death, nor life, nor angels, nor principalities, nor things present, nor things to come, not powers, nor height, nor depth, nor anything else in creation, will be able to separate us from the love of God in Christ Jesus our Lord - Romans 8:37-39