I think there is a number which tells you that it takes "x" many BTU to raise a gallon of water 1º. So if you have heat loss of so many degrees per hour, you are going to have to put all that heat back, sooner or later.
I don't think anyone has found that a timer on electric water heaters saves any money, either. Now, some utility companies will hook your water heater to OFF-PEAK timing, and you save on lower RATES, but not on less water used.
I have gone into apartments where the gas was off for 3 days, and the water in the tank was still warm enough to take a shower. Your unit must be in a very cold space if it loses 4+º per hour.