Thanks for the replies, guys. They are appreciated!
A couple of notes:
1) I apologize if it was somehow taken that I was suggesting Railo is unstable. That was not what I said, nor meant, nor intended to imply. We have *lots* of Railo sites running happily and smoothly. Just this one particular instance (a personal instance) is unstable.
2) I am definitely *not* dealing with much traffic on this server instance. Extremely little, in fact.
3) I do not intend to keep the server running at 512mb, as I plan to move a number of other sites over to it. I just don't want to throw more RAM at it simply for the sake of throwing more RAM at it.
4) Most of the time, there are no errors whatsoever that appear in catalina.out between Tomcat restart and crash. Generally speaking, the catalina.out entries are back-to-back startup details.
5) The only two errors that are ever showing up in catalina.out are a "file not found" that I cannot figure out why anything is trying to hit the URL that it's trying to hit, and an "file not found" on a CAPTCHA image that apparently is not being written to disk for some reason (likely a permission issue, but that's kinda weird since Tomcat has ownership of the directory).
The seriously odd thing is #4. No errors. I mean, sometimes I can start Tomcat up, browse to one of the sites, load the page, and then hit refresh and Tomcat has stopped. Other times it will run for a week or so with no hiccups.