Beach Chair Buddy Towel Strap
You could probably repurpose some tie-down straps you already have into the equivalent of Beach Chair Buddy towel straps. Or just get a length of nylon and secure one of those side squeeze buckles to it. But if you're not into DIY, or just want to support a good, well executed idea, Beach Chair Buddy is selling a 2-pack of their beach towel securers for a not unreasonable amount of money.
Simple, compact, and unobtrusive, Beach Chair Buddies strap towels tight to loungers, keeping them from flying off or bunching up in the face of wind, water, and your shifting, moving self. The strap maker say a single Beach Chair Buddy works better than two towel clips, and when used in pairs, one strap at each end of your towel, the only chance your towel has of blowing away is if your lounger gets carried off with it.