Water softner primer:
Water softners are rated at the grains hardness that they can remove. Typical 1cu/f resin can remove up to 32,000 grains before regeneration. You test your water, lets say it has 12 grains per gallon. You can run 2666 gallons of water thru it before regeneration, theoretically. In actuality, it's better to derate the softner to 21,000 to 24,000 max. The reason is, it takes a significant greater amount of salt to get the last bit of capacity. It's exponential. 6 pounds of salt will give you 20,000 grain capacity from 1 cu/f of resin. It takes 15 pounds of salt to get 30,000 grains from the same cu/ft of resin. 8 pounds will get you 24,000 grains. For best salt efficiency $ savings, use 6-8 pounds for regeneration. Using the same figure of 12 gpg, you'd have a capcity of 1666 gallons @ 6# before regeneration. Also, it is important that the softner regenerate once every 7 days regardless even if it hasn't reached capacity, or you run the risk of the resin becoming fouled.
Now, two problems could be occuring with your Kenmore. The most probably is you have a leak somewhere, check the flow indicator on the softner with everything shut off in the house. If you have flow, you have a leak. See if there is a garden hose left on with the nozzle attached, it doesn't take much. If no flow & no leak, then you have a timer problem. You can order replacement parts online from sears.