Under what circumstances players' ratings remain unchanged?

Obviously, one case when the post-game rating remains unchanged is when the game is unrated.

But what about a game that appears to be rated (no "unrated" comment) in either the list of games or in the game itself, the opponents are within 20 points of each other, the game is decisive, yet no rating change occurs? What could be the cause here?

If we are talking chess.com ratings, then my guess would be with the winner being the 20 point higher rated player and both having very small RD values. However, you would have to do the math to be sure.

Yup, chess.com ratings of just over 2000, Glicko RDs 49 (loser), 71 (winner).

 Sounds about right, with such a low difference between the ratings and the loser having a lower RD then the winner like that (more confidence in the lower rated players rating), it seems reasonable that the change could go close to 0, and then rounded to 0. (Looking at the math real quick it doesn't seem like it can be 0, but get pretty low).

I could be wrong, I don't know the glicko system in and out, so if someone knows better feel free to correct me.

Games of less than seven plies that end in timeout do not affect ratings.

There is a another timeout wrinkle. From a no policy situation, there was a ratings floor at five timed out games. After this there was a statement in the forums of an invisible ratings floor after five games, on the player timing out, for calculating the winner's rating.

It looks like currently the winner's rating calculation is based on the freefall rating of the player timing out.

There is a help entry concerning mass timeouts.

http://support.chess.com/Knowledgebase/Article/View/19/0/the-game-ended-and-my-rating-didnt-change-at-all-why

"A less common case involves users who have timed out in more than five consecutive games. Once this happens, the system assumes that they have simply abandoned the site for some reason. After five games have ended due to inactivity, we stop making rating adjustments on further time-outs in that user's games. This is to prevent arbitrary ratings inflation."

It is possible the above stated help entry is now stating the current policy and is actually being used. If so there will soon be quite a hue and cry.