ETA: Turns out I may have the wrong end of the stick.
Collabnet SVN stores its client certificate credentials not by using ssh-agent, but with gnome-keyring (or kwallet, or other platform-specific keyrings). This, in turn, leads to a longstanding open bug in Git where it won't try to use some of the various Subversion authorization providers that are available. This is a problem all over, and I'm not even sure who would actually be responsible for getting it fixed. So for now, it's not a SO problem.
I'm using git-svn to work against a subversion repo that uses client certificate authentication over HTTPS. I've got SVN set up properly to use certs, and command-line svn always prompts for my certificate password when I do a remote operation (because I could never figure out how to have it use ssh-agent to access credentials).
Now that I'm using git-svn, remote operations (like git-svn fetch) still prompt for a password each time, but this time using an X dialog titled "OpenSSH", which is identical to the ssh-agent dialog I get when I first log on each day. So it looks like git-svn is trying to use ssh-agent (yay!) but for some reason can't get access to the one that runs at session level (boo!) and thus needs to start its own... for each invocation of git-svn.
Is there something I'm missing that lets me "point" git-svn at the running agent and thus avoid typing a password every time I want to fetch?
/usr/bin/ssh-agentin my sessions file, which (as I said in the post) pops up a prompt for my cert password at login, then lets me SSH as often as I want without a prompt.