Most likely, the pump has stopped working. This is not repairable since part for the cleaning station are not available.
A replacement can be found at shaveroutlet.com
Braun Clean Charge Base 5783 Fits Types 5772 5774
I am not a razor consultant, but I would think something that old would not be wise to wet shave with:( did you try Braun 5563/manual in a google search? good luck!