This project provides a Flash plug-in for remembering the user's volume selection. It will store their preference in a SharedObject (aka Flash cookie), and use that value when the player is used again.
To use the plugin, you can either compile a SWF yourself by downloading the source code, or just simply grab the VolumePreferences.swf file from the project's bin-release folder. Once you have that, you can include it as a plugin to the player, or add it as a Module to the BEML for your player.