I have had one of those swimming pool liners in place for about 5-7 years. Occasionally a deer will step theu it and cause a leak. As dirt has filled in as a cushion,, less of this is happening. My present thoughts are that I needed more care in placing the pool liner tight to the ground. Or better yet, add a fabric or even old carpet under the pool liner.
Rubber roof material sounds like a much better idea.