It looks like I have a stale session open which is preventing me from umounting a disk image:

# w
 13:21:37 up 56 days,  2:51,  2 users,  load average: 4.30, 3.70, 2.23
USER     TTY      FROM              LOGIN@   IDLE   JCPU   PCPU WHAT
kfox     pts/8    192.168.8.90     Wed13   20:49m  0.02s  0.02s -bash
kfox     pts/22   192.168.8.90     12:04    1.00s  0.07s  0.00s w

Let's find the process responsible for my session (the "session leader"):

# ps -dN | grep pts/8
20524 pts/8    00:00:00 bash

Now we'll kill the bugger:

# kill -9 20524