Here's an interesting one:
Your Class D airport has a specially-established VFR arrival procedure because it's really really busy. Go to X waypoint, cross and descend to Y altitude while going to Y waypoint, cross and descend to pattern altitude and go to Z waypoint, cross Z waypoint and enter the pattern as instructed by tower. There are four of these depending on which cardinal direction you are flying from (northeast, southeast, southwest, northwest). X waypoint is the "entry" waypoint, Y and Z bring you into the pattern. The boundary of the Delta is between X and Y. During peak hours, tower switches from 1 to a split 2 frequencies, with the smaller parallel on the split frequency and the main parallel on the main frequency.
Now, you just happen to be coming down the arrival between X and Y with communication established on the main frequency, and they switch the freqs and advise you to contact the new controller on the other frequency. There is a delay re-establishing communications, and there are arrivals behind you coming in.
(1) Arrival or through flight. Each person must establish two-way radio communications with the ATC facility (including foreign ATC in the case of foreign airspace designated in the United States) providing air traffic services prior to entering that airspace and thereafter maintain those communications while within that airspace.
What do you do?