Ashiya (or was it maou-sama) sort of touches on this idea at the end of the episode where she has no one else from her home world. It's supposed to be a pretty profound isolation...I mean, as far as we can tell. Then again you wouldn't expect that isolation to cause her to do stuff like whimpering at their house, and you would expect more from a great holy warrior. You could half-explain it by her being obsessively fixated on eliminating Satan and wanting to return to Ente Isla (and this is also what will give the shippers romansu fuel)
If this is the angle they're aiming for I think it's really jarring and a letdown that she sort of wilts without her comrades, but as far as I can tell this is a comedic anime anyway and Maou-sama and Emilia will have UST. I'll give it some time; I sort of know they're going to fall in love or whatever, but hopefully she regains more of her warrior princess pompousness.
See, as funny as this show is at times one of the weirdest things for me was the first half of the first episode, because it makes a ton of shit pass by quickly: Satan and Ashiya getting a house, a bank account, jobs, all that shit must have taken a month or something, but the anime breezes through it. And the other thing is it almost looks like Satan fits in to Japanese society. We have no reason to assume Satan was so laidback or has sympathetic moments in the past. But in Japan he's changed, though it's under the guise of not blowing his cover so he can rule the world or whatever. The weirdass speeches seem more out of character than his adolescent persona.