I've stopped rips with a little drop of Super Glue. It'll smoke a little and melt the poly strands and then set up. It'll stop the rip from progressing. It's a ham-fisted fix I know. Not the best, but it's more permanent than tape.
We use to get some clear sticker material (the good stuff) and cut a circle through 2 sheets so there the same size. then stick one on each side of the screen covering the hole then get a plastic sguee guee the blue ones that are used for vinyl stickers (pre-masking) from a plotter. Press both side together with blue squee guee with firm preasure.