The difference, imo, was that it was always very obvious how Appleton wanted us to play, and I think we genuinely were very unlucky to lose some of the early games under him. Also, he came in midway through a summer transfer window to a club that was in a real slump and had to almost be completely rebuilt (Appleton alluded to having to completely change the club's philosophy in a recent interview). For those reasons I was always adamant that he should be afforded more time. Thankfully, Darryl/Ashton shared that view and kept him in the job.
Conversely, Robinson had a around a third of a season to suss out what was needed, and a whole summer to recruit accordingly. He failed to address some key areas and we're still suffering as a consequence. Additionally, after the first ten games I think most fans would have been hard pressed to explain what style of play he was trying to implement. We were shipping horrendous goals game after game and rarely looked likely to score save the odd bit of individual brilliance. For all of these reasons, I eventually conceded that he needed to go.
All that said, I think he's done a good job of weathering the storm. The defence, which appeared beyond repair, seems to have been fixed (not least as a result of Mosuinho being deployed just in front of them, something that most fans had been calling for for many weeks may I add!!). I think that the poor start made him carry out some self-reflection, and thankfully he seems to have learnt his lesson. As long as the current form continues, and he continues to apply a more measured approach to his management in general, I'm more than happy for him to stay.