Eggman is married to his work.

Like spongebob, or jason vorhees, eggman doesn't go this way, swing both ways or go that way, he is too much of a workaholic to really care about romance. I even perceive him as aggressively celibate in an attempt to be more like his beloved machines, I,m disappointing his admirers, but that's my theory. He isn't totally asexual, but he gets his kicks from furthering his own power.