when I had that, it was because the rubber seals on the pistons that operate the valves were scaly and had jammed down instead of popping up when finished.
My local water softener co (they also deliver my salt) sent a man round who dismantled the control mechanism, replaced some parts, reassembled with new seals and silicone grease. Might have been about an hour's work.
Some of the parts are made of plastic and screw together, if the threads jam they may not unscrew without breaking. If I was DIYing I think I would use plenty of silicone grease on all moving parts, and probably PTFE tape on any threads.
My old softener was very old, I don't know if silicone grease was being used when it was made. Eventually it went wrong again and I changed it for a reconditioned one. Both were/are original Permutits (the brand name has now been sold and is not as good) and the faults occurred at intervals of about 10 years.
p.s. some of the operating mechanisms and valves are an assembly by one wel-known company whose name I have forgotten, so if it is standard I would have thought parts or a new assembly would be available. The very cheap ones in DIY sheds are I'm told throw-away when faulty.
p.p.s. I see from my supplier's website
http://www.aquadition.co.uk that the Kinetico has two tanks and regenerates each with softened water from the other, which they say prevents the mechanism and valves from scaling up. I have no connection with this company except as satisfied customer.