I believe that the recliner is original, so I'm not surprised that the screws that hold it to the floor are coming loose. I'm thinking that just adding more screws ought to let it last another 24 years. Any suggestions for the proper size of screw? Anything in the way? The chair is immediately forward of the door.
David,
Pull one of the screws that is no longer holding. Go to the next larger diameter, or fill hole and redrill.
One can use a (or more) wooden matchstick dipped in yellow carpenters glue to fill most holes before re-drilling.