I had similar experiences. I ended up wrapping the bottom half of the exposed laces in duct tape. As for the side, that part of the TC is notorious for delaminating even under normal climbing conditions. I would use rubber cement / barge cement proactively but still have the problem. One of the reasons I switched to Generals.
Look for Kiwi round Outdoor laces black yellow. I replaced my TC Pro laces with these and they match well. You wouldn't even notice if you weren't looking