I tried putting some foam on top to help hold it down more tightly and securely. (See Fig. 2)

That worked for about a week, maybe, but after that . . . the same old thing again. The low beams have always worked fine, but eventually the passenger side high beam will go out. Today I pulled the relay and pried it apart, by carefully, yet forcefully, sliding two table knives past the tabs on opposite sides of the case. (Fig. 3)

That left one more, which when pried away causes the internal circuit board to slide out. Close examination of the circuit board (Figs. 4 & 5), where it connects to the pins that fit into the slots on the fuse box, revealed that the two solder joints on the two pins at the extreme edges of the board were cracked. It appeared the center one was, as well. In the photos below, the circuit board is shown up-side down and the pins referred to are at the top in the photos:

Fig. 4:

Fig 5 (not a very good camera I am afraid). The extreme left and right solder joints had visible cracks upon very close examination. I re-soldered these, and the center one which appeared to be possibly cracked:

Using a 30 watt soldering pencil, heat the pin and press some .032 inch diameter 60/40 rosin core solder against the crack in the joint. It will take time for the pin and solder to conduct enough heat to the solder for it to begin to flow into the crack. You may try to just re-melt the solder, but often this will result in a dull solder joint, which is in fact a cold (or non-conducting) solder joint. If you are an accomplished solderer, a 50 watt gun or pencil may work better, just be sure not to damage any components on the circuit board with the higher heat. You can use heat sink clips to help with this.

Upon re-installation, everything works fine.