I owned a rotary engine and it was a wonderful intoxicating thing.
They get a bad rep because they're not the kind of engines you can just service at their service intervals. You need to treat it like your baby. If you're the kind who doesn't pop the bonnet at least once a week it's not going to end well. If you're the type who only replaces components when they totally fail, rather than when they're past their best, it's going to end badly...
They need looking after, but the rewards are well worth it.
They usually fail early through either apex seal failure or rear stationary bearing failure. Both are due to poor lubrication, which can be improved greatly by an owner who cares. It's a complicated subject discussed heavily on rotary car forums like the RX8 owners club where I'm a member.
Wrong oil, thrashing it before the oil is up to temperature, poor ignition coils, etc can all contribute to early engine failure, but if looked after properly (also using 2 stroke oil as premix boosts the lubrication of the apex seals and a thicker grade oil that clings to the stationary bearing better) will help the engine live as long as a piston counterpart.
If both are treated badly, I'd suggest a piston engine would usually outlive the rotary, but you'll get far more smiles per gallon with the rotary than the equivalent power output piston engine. They're really an enthusiast only engine, which is why they're seen as poor engines by non-enthusiasts who don't look after them, and you won't convince a rotary aficionado that there's anything better.