This is awkward to stage out, certainly. Can you see Darcy sneaking out the servants' staircase? Can you see him announcing his intentions to the room prior to leaving? Can you see him not being missed, if he simply left?

The best I can suppose is that he left after hearing Elizabeth was ill, but not in a way that would make anyone suppose his departure was connected with the news. (They did take potty breaks during the Regency, I assume?) His interview with her was not long, counting everything, and his agitation when he returned and excused himself made all think he must be taken slightly ill.