What you have described is nearly identical to a the long term, but only intermittent problem I have had with my 5600sxt valve over the past 3-4 years. Long story short...I could never figure out why no brine refill after regen I would observe sometimes, but not all the time. I investigated all the usual culprits from the various sites and even replaced the motor. The problem always came back. I have finally ordered 2 new micro switches and will see if that eliminates problem once and for all. While I don't know the cause, I have been able to observe what actually occurs with the valve when it skips BF. After a regen starts, the valve cycles thorough BW. After BW is complete, the motor kicks in to advance to BD. Those two regen stages are fine. The problem starts when it advances to RR. The display shows that is in RR, but that is not what happens with the gears and motor. The motor engages, but quickly stops. In other words, the valve (pistons etc) is still in BD, but "thinks" it has advanced to RR. So the valve is now "behind" one stage of the regen cycle (as far as the main and brine pistons positions are concerned). Once the timed setting for RR is complete, the motor kicks in and advances to the next phase, which is supposed to be BF. Again, this is what the display shows. BUT, remember the motor never advanced the gears (and thus the pistons) for RR to actually take place. Therefore, NOW the gears and pistons advance to RR (even though the display shows BF). After the timed setting for BF is done, the motor and gears cycle all the way back to the end, QUICKLY PASSING THROUGH THE PROPER GEAR/PISTON POSITIONS FOR BF.
I know the above sounds confusing. In other words, I have one place in the regen cycle where the motor does a quick start and stop. It always happens after BD when RR is supposed to start. At that point the gears/pistons are out of sequence (by one stage) even though the display thinks everything advanced properly. Since BF is the last phase, but the system "thinks" it's already done, the motor/gears return back to the service position skipping through their BF positions.
I was able to observe the motor and gears doing this by removing the power head and plugging it in on my work bench, starting a regen and advancing it through the regen stages. I saw the problem occur (quick start/stop between BD and RR) about 1 out of every 4 times.
I believe you may be experiencing the same problem. Your valve circuit board may have more advanced programming and is throwing an error code because of the cycle/sequence skip.
I am hoping replacing the micro switches will finally solve my intermittent problem. Replacing the motor didn't do it!