Some fabrics, like Goretex allow air to pass and block water by a non wettable woven grid, others have a continous block that will not pass air or water. I assume a pond needs to continuous block. If the fabric and the blocking agent will not rot or be attacked by soil bacteria, in an underground milieu it will last a long time, failure will be by assorted holes, of whatever size that gradually increase the leakage cross section to the maximum allowable leakage.
Permanent membranes for this use are usually dacron or nylon or other synthetic densely woven fabric that has one or more impervious and continuous layers of a synthetic rubber or plastic. The woven fabric must be strong enough to withstand the weight the cloth must bear and the sealing layers must resist the hydrostatic pressure. Often they are made in several layers and the crossing angles vary to make sure there is no weak direction along which it can tear. The bed in which is laid is also tamped and pack to make sure there are no voids to collapse or any sharp pointy things that can pierce to make sure there will be no leaks for decades - more time = more $$.
And it all works very well until the wading birds think there is something under the fabric at water level and punch holes through the fabric lowering the water level and the whole process repeats itself.
Had it happen to turkeys nests, colloquial name for above ground ponds, in the desert, for they just loved to explore the underside. Good luck with your endeavours.