Not to admit to my geezerness, but I still read Parade magazine!
Here's a link to an ad for a flexible screen door- more like a curtain, really, with a magnetic closing system. Magnetized at bottom, too...might keep the pesky mice out!
$11.99 plus $ 4.99 S&H (with value code from magazine :XAR 643)
Four Corners - Magnetic Bug Screen