Obviously we are on statics. I assume this starts off with places where the screen starts to sneak off the frame. Usually still quite a few more uses before it would give up completely. I used to have the same issues.
I would just get a tube of the screen frame glue and the spray activator and give the ones starting to get a loose spot or two a shot of both to re-glue.
I'm thinking that might be less time consuming and possibly less messier than using a caulk seal, but just my 2c.