If you're brewing 1000ml you will need to incorporate some form of *constant* stirring method throughout the entire brewing process. My advice would be to NOT brew such large quantity without constant stirring.
You will also need to remove the electrodes at regular timed intervals - each 30 minutes - to wipe them clean before resubmerging them. You'll still get electrode discolouration, but it's kept under much better control.
Why is it turning dark? Going on your brewing process and equipment information, there will be a lot of particles forming over time your solution is in storage. Your unit is a non current controlled unit and is allowing current to run away exponentially over time during brewing process thus speeding up the silver deposition rate into the water. In short, the brewing process gets out of control. I assume you are not allowing that copper wire to enter the water along with the silver electrodes?
Why is ppm dropping? Drop in ppm is normal over time as some of those ions form into particles, but in your case you have large quantity of ions present which are converting to particles. And you probly have some of that electrode buildup entering the water as well during the brewing process.
And if you improve on your brewing methods you can throw that filter away too, cos you won't be needing to filter anything. Keep that electrode discolouration to an absolute minimum with reasonable diligence. I would also advise you install a 38 ohm resistor in your unit circuitry to control/limit current.