Rain Soft System causing lose of well system prime

Hi - I have a 20 year old rainsoft system that recently started causing a loss of water pressure when the mineral tank back flushes. It does not loose pressure when the brine tank back flushes - just the mineral tank. The presssure gauge on the system generally shows 50-60psi. Water pressure is good throughout the day and night regardless of whether the shower, the dishwater or the clothes washer is running. The water pressure tank is showing 45psi with a tire gauge. The pump comes on around 40psi and stops around 60psi.

The rain soft guy says that the pressure switch may need to be replaced and wants us to call in a plumber. I think it is the water treatment system because I can hear the back flush starting in the middle of the night and then I immediately hear the pressure drop and the backflush process stop.

Do you have any ideas whether to focus on the water treatment system or the plumbing?