Jared - a lot of strops, particularly the ones that are tanned to have a waxed/oil finish (latigo, some english bridles, etc) will leave a buid-up on the razor which is quite normal.

I think that the loss of draw is a combination of the natural 'nap' of the leather and the slight texturing of it being both smoothed down by the mechanical process of stroping and in the case of waxed/oiled leathers by the redistribution of the oils and waxes.

As you have found, rubbing the strop with your hand helps raise the nap again. Rubbing a waxed/oiled leather with a balled-up slightly damp non-fibrous cloth helps with waxed/oiled strops, too.

I wouldn't worry about the leather drying just yet - latigo doesn't need any special treatment for ages, maybe many years. Rubbing with your hand is all that is required.

Regards,
Neil