lightdm crashes during normal operation with no obvious cause

This has happened several times in the last few weeks, including twice yesterday. There is no obvious user action that triggers the crash: the first crash yesterday, I was composing an e-mail in the GMail pop-out editor; the second I was editing a config file on a remote server via SSH; previously, the crash has happened while I've been just reading something on the screen, not interacting with the computer at all.

The symptoms are a non-responsive display, with the exception of the mouse pointer. I'm not even able to switch to a different vt - just get a black screen. However, I *am* able to SSH into the machine, and when I did so yesterday I tried:

 * killing compiz
 * restarting the unity7 upstart job (my windows flashed briefly on the screen, then I got the login background)
 * restarting lightdm

The latter action got me to a login prompt, where I was able to login and start a standard desktop session and, thankfully, resume my screen and tmux sessions and not lose any work.

ProblemType: Bug
DistroRelease: Ubuntu 14.10
Package: lightdm 1.12.3-0ubuntu1
ProcVersionSignature: Ubuntu 3.16.0-30.40-generic 3.16.7-ckt3
Uname: Linux 3.16.0-30-generic x86_64
ApportVersion: 2.14.7-0ubuntu8.2
Architecture: amd64
CurrentDesktop: Unity
Date: Wed Apr 8 14:55:47 2015
EcryptfsInUse: Yes
InstallationDate: Installed on 2014-07-04 (277 days ago)
InstallationMedia: Ubuntu 14.04 LTS "Trusty Tahr" - Release amd64 (20140417)
SourcePackage: lightdm
UpgradeStatus: Upgraded to utopic on 2015-01-31 (66 days ago)