Above Ground Pool - Pinhole Leaks
First of all- Good on you for patching it rather than dumping it in the landfill!   

I had the same pool problem last summer, several pin hole leaks.  What is cool is you can patch them underwater with the patch kit.  (I recommend applying the patches on the water side.)  The real tough ones are holes on the bottom of the pool.  They aren't easy to find without goggles and slowly crawling along the bottom of the pool.  I only found mine when a tiny piece of dirt was being sucked into the leak.  

As for an answer, your sides will no suddenly tear because the material on the side is rip stop. (nylon threads embedded in the vinyl).