Under certain circumstances, the modal dialog will simply disappear instead of fading out (even though it successfully fades in).

The example in the documentation is what it should do (fade in and out).
https://angular-ui.github.io/bootstrap/#/modal

Ironically, the plunker link it generates shows the modal not properly fading out. I've saved my own to serve as an example here:
http://plnkr.co/edit/lmFTpQtfgV6qB4AuFrXj?p=preview
[Edit from @chrisirhc to reduce confusion: Please take note that the above Plunker does not include angular-animate. As such, no animations should be seen. This is a new requirement for animations, see README.]

I have the same issue in a separate project of mine where I am handling the modal differently but have the same bug. I can provide the 2nd example if it would help but I imagine the plunker should be enough.

The bug appears to be browser independent as it occurs both when I use Chrome v42.0.2311.135 m and in the developer edition of Firefox (39.0a2).

UPDATE: Note that the plnkr is using the latest version of angular-ui (0.13.0) and the latest supported version of angular (1.3.13). This is not about angular 1.4.