If you have access to a field strength meter and know how to use it properly (older models are more difficult to use, but that is usually what is floating around outside of radio stations), you could estimate the skywave present by looking at the cyclical fluctuation of the groundwave. Say you have a 100 uV/m groundwave when no skywave is present. Say in December when other stations show daytime skywave, it goes up as high as 110 uV/m and as low as 90 uV/m in a cyclical fashion in a time when conditions are noted. The skywave would then be 10 uV/m. That won't be consistent, but it does show the existence of skywave at very low levels, all other things being equal.
I don't think there is any nonlinear diode like action from reflecting layers, though some have speculated on that. The skywave is just too weak to be detected at low powers. You might the above if you have the equipment. That may reveal a very weak skywave but I've never heard a carrier just completely and suddenly fade out completely, except on perhaps a crystal radio. It's gradual.