I've noticed that NOW the bottom is getting brittle, but, like you, I'm leaving it in place as a tarp over the sand.
On the chemical side, I'd never use a Nature2 because, while it helps control algae, it adds metals. While it's expensive, an SWCG will allow you to do the same thing.
Are you careful to watch your CYA levels with the Tri-Chlor? Remember for every 10ppm of chlorine it adds 6ppm of CYA.

My sand filter is fine and the plastic tank shows no sign of brittleness or UV breakdown. It's always been covered over the winter, and, for the last several years, been under the deck addition (where the deck chairs are). I'm still using my original sand, no problems.