I bought one of these about six or seven years ago. Still no tears and my 75 lb dog loves to burst through it at full speed.

https://bugoffscreen.com

It's a nylon mesh but maybe a heavier one then what you got. Uses a spring tensioned rod to mount in the doorway which needs to be readjusted every so often and sometimes the dog will step on the screen and pull it down partially but no rips.