Does an electrolytic capacitor degrade each time it receives reverse voltage?
There are many types and subtypes of electrolytics, I will concentrate on those most common for hobbyists: the liquid electrolyte aluminum one.

Most details can be read in the corresponding wikipedia article  but in short:


The cathode oxide layer can withstand up to 1.5V of reverse voltage
it can receive permanent damage earlier, but 0.5V is deemed safe


When applying too high reverse voltages for too long, one of two things can happen:


gassing makes the cap explode
dissolving of the oxide layer shorts the cap


These numbers and probability of failure mode can greatly differ when going far outside of what is considered "room temperature".

Even short application of too much reverse voltage can permanently damage the capacitor. Sometimes the self healing abilities can reverse this a bit over time, but there will be permanent damage.

Some ways to see the damage is:


increased leakage current (due to partly dissolved oxide layer)
decreased capacity (due to self healing of oxide layer holes)


Other types of electrolytics have different kinds of behaviour, but most people deem short exposure of up to 0.5V reverse voltage ok. This is why a lot of LCR meters measure capacitance with 0.5V AC regardless of any polarity.