When your water softener runs but does not soften the water, and the salt level in your brine tank does not seem to go down you may have a problem known as a salt bridge. A salt bridge is a hard over-crusting of the salt in your brine tank covering or spanning over the water.
When a water softener stops conditioning water the problem is that something is stopping your water softener from regenerating. The regeneration cycle of the resin bed is where the water conditioning occurs.
Assuming you are not out of salt the problem may be one of a few possible problems. There could be a salt bridge that has occurred, or a crusted salt plug or other blockage between the brine tank and resin tank, or there may be a problem with the control valve (if an automatic water softener). Any of these problems may be stopping the unit from going through a regeneration cycle.
The most common problem however may be the salt bridge. A good source on how to repair this problem is found at this page from the Canadian Salt Company Limited.