After busting my fingers off configuring quite a few mods (and applying the configurations for each) the configurations reset as soon as the server is launched. When I return to the mod list, all of the mod configs have been reset to their defaults.
Alternatively, I tried saving the configurations of mods for the game itself instead of a single server. Before launching a server, I also decided to double-check the mod configs and hit "Apply" to each of them. This worked for one gameplay session, but the configs were reset to defaults as soon as I shut down the server. This does not happen to client-only mods, however.
1. Make configurations to a mod 2. Hit "Apply" 3. Begin or join an existing world with those configurations 4. The configurations will have no effect