I think that social conflict can only continue so long as there's something keeping both parties involved in it -- and perhaps more importantly, only so long as neither party wants to transition to physical combat. In many of the examples above, the scene would probably resolve along these lines:
Player: "I try to convince Cthulu to go home and leave me alone." <rolls> "Oooh, a legendary success!"
GM: <marks off the appropriate stress> "Hm. Although Cthulu seems genuinely impressed by your arguments, he responds by trying to eat you. We now shift to physical combat."
In the infiltration example, the gang member (cop or no) has no motivation to stay in the argument. Sure, he might gain a Reputation for being rude by slamming the door in your face (ie, conceeding the fight by accepting a social consequence), but will he or his fellow gang members really care? Of course, the players could force the issue by sticking their foot in the door, but again, this could well provoke a transition to physical.
If the player had placed an aspect on the doorman (via maneuver or inflicted as a social consequence), he could try invoking an aspect to trigger a compel. For example, say he placed Thinks the cops'll get here any minute. Against a normal gang member who had something to fear from the cops and who see the player's entry as a way to somehow avoid such legal entanglements, the GM might well accept the compel and have the gang member respond accordingly (which would also resolve more or less as a form of concession). But against the cop, the GM could just say there is not a compel-worthy circumstance present, and not accept the invoke attempt -- probably with the results mentioned in the paragraph above.
