What should be done to continue a long-distance contact when the MUF for that path decreases due to darkness?

The Maximum Usable Frequency (MUF) is highly dependent on solar ultraviolet radiation. When the sun goes down, ionization levels in the ionosphere decrease, causing the MUF to drop along that propagation path. If you are operating near the MUF and darkness falls, your current frequency will likely become too high to be refracted back to Earth, causing the signal to pass straight into space. To maintain the contact, you must tune to a lower frequency band that rests below the newly reduced MUF. Switching to a higher frequency would only make the problem worse, and changing antenna characteristics like takeoff angle or beamwidth cannot compensate for the lack of ionospheric refraction at a frequency above the MUF.