At there are apex seals at the ends of the triangular rotor that need to stay in contact with the sides of the combustion chamber to prevent blow by and get a complete and efficient burn, so they have springs in them that press them against the walls of the engine. However, metal (or ceramic) to metal contact like that means that they also need to stay lubricated. Unlike the a piston engine's piston rings, there isn't a real easy way to get oil to where the seal is, so you must inject oil into the engine where it will be swept into the combustion chamber. Even then, the apex seals eventually wear out. They basically require a complete engine rebuild to replace.

The combustion chamber is quite long compared to a traditional piston driven engine, and that, combined with the apex seal blowby problem and oil burning problem, means the engine is actually quite inefficient. Rotary engines do not typically have good gas mileage. An RX-8 has a 1.3 L engine but only gets 18 mpg (13L/100km), although it produces 210–235 hp (157–175 kW). It's this poor efficiency that caused Mazda to cease production of Wenkel engines in 2012. They can't pass emissions tests. The Wankel rotary engine (https://en.wikipedia.org/wiki/Wankel_engine) actually has comparatively poor fuel efficiency. It just also has a high power to weight ratio.

Additionally, the combustion chamber is on one side of the engine, meaning the engine heats up unevenly. That makes it wear unevenly and can make it difficult to get a seal that will work on both the hot side and the cold side.

So, the problems with the Wenkel engine:

1. Lubricate a part that you can't reach and is going to be constantly bathed in fire.

2. Make the combustion of a fuel/air mixture in a long, wide, narrow chamber as efficient as the same fuel/air mixture in a much more ideal cylindrical chamber.

In a piston engine, the cylinder walls and the sides of the piston form the seal that keeps the combustion contained. You have a lot of metal-oil-metal surface area to work with here, so it's relatively easy to get a good seal.

On a rotary engine, you have comparatively thin apex seals. These wear out quickly, and make it more difficult to get a good seal. Additionally, combustion always happens on the same side of the engine housing, so you tend to get warping, which also makes the sealing problems worse.

Reciprocating engines definitely have their own problems though (e.g. valves), and here I think you can safely argue that our longer history with them has helped a lot.