I've noticed that if I have several chickens incubate eggs at once, some of the eggs get forgotten about - i.e. I'll get 3 animals out of 4+ eggs. Right now, the fix seems to be to incubate at most 2 eggs at a time, but that's a little irritating.
If you read carefully what the chickens say to you when you give them an egg they tell you not to leave because if you do the hatched egg will be lost. Your best bet is to keep all incubating chickens on the screen for the full minute to minimize the chance of that happening.
So, there is something up with the chickens and the incubating that we are looking at.
In general, Skwid is right- you have to stay put when you give the chicken an egg, and wait about a minute.
But-
In some cases, a chicken will appear to be stuck walking in place, though it's not obvious. You give the chicken the egg, chicken keeps walking on the spot. And walking. You give her another egg, and nothing changes. We're looking into what's happening with those chickens.
I just incubated an egg and the chicken disappeared completely. It still finished the process — I received a piglet — but it just vanished into thin air.