Water Softeners and Air Filtration Systems - Sears Demand water softener salty after regeneration

I've got a Sears Demand water softener (model 625.348490). When I bought the house 3 years ago it was unplugged. I didn't mess with it until about a 2 years later, so it sat unused for at least a few years I presume. When I finally got to it, I did a thorough cleaning of the tank per the manual's suggestions. I plugged it in and it seemed to work for a short time. Eventually the motor began to constantly click, which meant that it could no longer turn the rotary valve. I assumed the seals were shot so I ordered all new seals/o-rings for the rotary valve assembly. It worked again for several months and then no soft water again. On further inspection, the seal attached to the bottom of the float had become unattached which in turn would not let any brine to be sucked out. I replaced the float and also went ahead and replaced the nozzel & venturi and associated gaskets, which were pretty much shot.

As of now the unit works as it should. All cycles complete properly and no errors are reported. I'm getting soft water now, however after a regeneration the water from the faucet is always noticibly salty in the morning. After running the water for a while the saltiness does go away. I should note that this is not a new thing, it has been this way ever since I first got the unit working.

Does this signify that something is wrong with the unit? After sitting for several years unused is there some sort of resin issue that needs to be addressed? What are my options, can I replace some more stuff and have a like-new softener or is it time to look at a replacement?

Sounds like the resin is bad. To check, get some resin and pinch it bewteen your thumb and finger. If it smaches up, it's bad. Also, from what you have said, sounds like you are on city (chlorinated) water. Chlorine really effects the water softener.