To make a save backup, you will need to log in via console. The details of how to do this vary by server and operating system, but on windows you will typically use the Putty app, and in OS X you will use the built in Terminal.app. For server details, see your server's specific instructions. The following pictures step through what this looks like for CBRO on OS X.
First, ssh in in your preferred way (I have already downloaded the CBRO ssh key and saved it in my .ssh directory):
Then, login as your character and select the dcss version you were playing under:
Select “A” (capitalized) for the Advanced options menu:
And finally, select “B” (capitalized) to back up your save. This will give you a link:
Copy the link and share it with a developer somehow, ideally on mantis. This link is password-protected and backed up saves can only be accessed by developers. This save backup will exist past your game, so you can keep playing, quit the game, or whatever you want.