So do I, because like you, I have my doubts that entropy continues to increase with each bounce.
I've read -- this is 2nd hand only -- that back in the 1930s, someone named Tolman showed that entropy increase was inevitable for a continuously oscillating universe. The reason I'm dubious is that I don't know where the "lost" energy/information would go. It's all got to be preserved in a crunch for yet another performance of the cosmic show. Or so it seems to me.