Do long periods between regenerations (say a month) have any negative effects on the softener?
A water softener should be regenerated when the softener has reached its capacity and is unable to keep exchanging the hard ions for the soft ions. How often a water softener regenerates is dependent on how many grains per gallon of hardness is present in your water and the (size) grain capacity of your water softener. If the capacity of the water softener is 40,000 grain, and you have 10 grains per gallon of hardness, then your softener would regenerate after 4,000 gallons of water had passed through it. How quickly you would use 4,000 gallons of water would really depend on your water usage.