the only time i've had the button fall off is when a multifuel has sat a long time and as Floridianson said, it's probably because the plunger is sticky and created a gap .. My thoughts are that and,,, perhaps the button was also stuck to the opposing mating surface and got pulled away from the retaining clip .. The clip isn't strong at all .. What can promote the problem is an operator who did not leave the fuel shut off lever pulled out after shut down and the truck sits long enough for the fuel to gum
To answer your final question, i don't believe it to affect the button whether or not you turn it over by hand .. The button situation is a crapshoot IMO.. Regular use and fresh fuel with added lubricity is what's beneficial to the button and fuel system..
However, turning over by hand is a beneficial check for hydrostatic lock in any injection engine that has sat a long time and one that you are new to ... After that when an engine checks out to be okay and you crank it the usual way, an operator should always pre-crank a multifuel with the engine stop lever pulled anyway, per the TM and PM Magazine articles. Hydrostatic lock is uncommon, however the second it happens you may immediately regret not following procedure