Since my switch to Gentoo, my DVD drive has decided that it really prefers to stay closed. In order to further its goals in this area, it was closing seconds after opening, making swapping out disks nigh impossible. After a substantial amount of work to make Google return a result that even remotely resembled my problem, I came across a relatively recent post in the Ubuntu forums where a number of people had a similar problem - curiously all on Macs with Pioneer DVD drives (a hardware configuration which most definitely does not resemble my setup) - from which I followed a link to a Redhat bug report which was slightly older than the Ubuntu post. Between the two sites, I was able to piece together that this problem appears to be a kernel level bug, which has a curious fix.
If you are having a similar problem, a temporary fix that will allow you to check if you are suffering from the same problem is to run the following command as root:
sysctl -w dev.cdrom.autoclose=0
Running that command on my Gentoo system allowed me to open the drive for an indefinite amount of time, rather than the second or so that it had previously allowed me.
To make the fix persistent, open the file
/etc/sysctl.conf for editing and add the following to the end of the file:
dev.cdrom.autoclose = 0
And with that, your DVD drive should cease to bother you - or at least have one less annoyance.
Now I just need to convince Nautilus that the DVD drive not only exists, but that it should automatically mount it for me when there is a disk in it.