Repair is almost always the least expensive option, providing it is successful on the first try. If you’re able to positively determine that the visible hole you see near the waterline happened when Uncle Fred tripped and poked the skimmer right through it last weekend, you’re in pretty good shape if the liner is otherwise robust. Depending on your liner type, a small patch and some glue or tape are probably all that’s required.
If you’re unsure where the leak is, or even whether it’s just a single leak, things get more complicated. Emptying your pond is a laborious process and one you don’t want to have to repeat. Waiting for a pond with a relatively slow leak to level out at the lowest point doesn’t promise a good experience for your prize goldfish. Multiple leaks at several levels require repeated tests, repeated emptying, and all the time and labor that entails. Then, you need to ask yourself why there is more than one leak. Is the liner aged? Is it a poor fit for the conditions? Is it simply a cheap liner purchased to save a few bucks when the owner built the pond? Any of these circumstances require replacement unless you relish the idea of annual repairs. Don’t forget that the more patches you apply, the weaker the liner becomes overall, with more potential sources of failure.
If you’re dealing with age and UV degradation, replacement is the clear answer. You can’t repair those conditions, and any attempts at patching will simply further damage the surrounding material. Epoxy, probably the most common repair adhesive, actually erodes the surrounding material as part of the bonding process. That just doesn’t make sense for an already weakened liner.