Will I face issues re-entering Thailand without a valid visa after my retirement visa expired?

There's no explicit specified limit but that doesn't mean you can do it as many times as you like, they may question or deny you if you do it too much.

Some people like oil workers or people living in a nearby country do similar to your proposed pattern for a long time with no issues, others get questioned.

You should have the three required items- 20,000B in cash, hotel reservation, ticket out.

Paul Richardson your retirement visa allowed you to do the many seven day visits.

Its now a new ballgame for you. Your every three weeks entries most likely will prompt Thai Immigration to question your many stays.

Paul Richardson I don't see why your expiring retirement visa creates a problem.

I view your many ..every third week.... repeated seven days visits ...are the real potential problem causing Thai Immigration to question you.