It's a simple, clean unregulated supply. Supply voltage will drop with the battery drain. Measure across the battery terminals while the preamp is operating to determine the actual Voltage under load.
I suggest using Powerex 9.6V rechargables (they now offer an Imedion branded low self discharge version) which measure something like 10.5V or more (open circuit) when charged and the battery will probably not drop below 9V in typical use.