For the most part they're pretty tough. However, tranny rebuilds get new or remanufactured converters because they do have wear parts, the blades can fatigue and crack and bend or break, and the stator (the magic part of a modern converter) has a one-way clutch or sprag that if malfunctioning or failed can cause your car to be a real dog. The stator is the part that makes it efficient and provides torque multiplication. Either type of failure makes it feel like your car is dragging an anchor. Which failure it is will affect low or higher RPM operation. So, they are cut open and freshened with the trans, with new wear parts, new sprag, and new impeller blades or fresh brazing.
Note HP converters will use bearings instead of washers (stock), and due to the sensitivity of teh stator for efficiency, it is usually inadvisable to get a "high-stall" converter that has an improperly modified or hacked stock stator. While cheap and easy to do it that way, those are the converters that mushy and hot at less than stall, where a properly-designed increase in stall will feel much like a stock converter in normal driving, but will flash RPMs higher when you punch it.
One last tidbit - be aware that high-power can balloon a converter, but so can RPMs. A stock 12" converter shell can balloon as low as 5500 RPMs, and an 11" at 6500. A ballooned converter pushes the hub into the trans, causing damage. Many drivers are not aware of this, and a transmission failure after a redline run is often from ballooning, unless the converter is designed or modified for the higher RPMs.
Converters are the heart of the driveline, and it can make or break the performance of an otherwise good engine/chassis combination. Check your FSM for testing procedures on your converter. Most of the tests and diagnostics also apply to aftermarket converters.
Common converter wear and failure points: