Sears water softener problem

Our Sears model 625.348732 water softener, now 10 years and 3 months old, seems to be filling the salt storage tank with water when it is not in the fill cycle.
A few days ago I noticed it was about half full during the day, although it is set to recharge only on Monday at 2:00AM. Yesterday (Friday) I took it apart and cleaned the venturi and brine valve. Afterwards, I scooped out all the water I could reach, then manually cycled to the Brining stage to pump out the rest. After this was done the water was down to about 4", where it should be after brining.
Much to my surprise it was almost half full again this morning, Saturday. I rechecked the programming, verifying that it is only supposed to recharge on Monday at 2:00AM. This means something is leaking, allowing water to flow into the salt tank other than during the fill cycle.
What can be causing this? My thoughts are (a) the resin tank is leaking, or (b) the valve is leaking internally. I'm wondering if it's time to think about replacing the unit.

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