I have a screened in porch that I repainted and replaced the screens on last year. One section of the screening has torn through the staples I used to secure it. Needs to be stapled back again under the furring strip that covers it. Is there anything I can do to prevent it from tearing through again or secure it better? Thanks. It’s black fiberglass material I believe.

I use the same method on my screen porch. I just space the staples very close and cover it all with screen molding. I've had to replace the screen due to tearing in two panels over 30 years. I have one that needs to be retacked along an edge now.

My son just added a screen porch and they used a plastic/pvc trim that was grooved and splined it .
It looks great and much better way of doing it than staples. Home depot sells the Screen Tight system but his was for the inside of the framing and Screen Tight loooks to be a flush mount.
Splining gives a professional and neat appearance and should be easier to replace.

Duct tape.

Could it have been pushed on and damaged?

Don't stretch it too tight, don't overdrive the staples and staple close together. That is about all I got.

I had good luck with the fiberglass screen from Lowes so far on a 14x16 Gazebo I built. Still looks good as new after 7 years.

staple it , fur strip it ,use hair drier to shrink it and slap people who lean against it.
or use hardware cloth to re enforce if slapping is not an option

Might try something like Elmer’s glue in the mesh that gets covered. Let it dry, staple in place, cover with trim.

Glue might help strengthen the screen and share the load over a greater area, resulting in less tear through of the staples.

I agree with 45 Cal. Use fur strips, preferably aluminum. No maintenance required.

Jim