It is worth mentioning that any electronic device used to control a pump is only acting a s bridge between the battery and the control. The controller its self is using very small amounts of energy. The pump is taking somewhere around 99% of current drawn.
A well maintained battery used as the manufacturer intended can give a very long life, A less well maintained battery may have a much shorter life due the the discharge/recharge cycle and how often the battery is drained lower than the manufacturer recommends
A car's battery is designed to provide a very large amount of current for a short period of time. This surge of current is needed to turn the engine over during starting. Once the engine starts, the alternator provides all the power that the car needs and slowly recharges the battery. So a car battery may go through its entire life without ever being drained more than 20 percent of its total capacity. Used in this way, a car battery can last a number of years. To achieve a large amount of current, a car battery uses thin plates in order to increase its surface area.
A deep cycle battery is designed to provide a steady amount of current over a long period of time. A deep cycle battery can provide a surge when needed, but nothing like the surge that a car battery can produce. A deep cycle battery is also designed to be deeply discharged over and over again (something that would ruin a car battery very quickly). To accomplish this, a deep cycle battery uses thicker plates.
A car battery typically has two ratings:
CCA (Cold Cranking Amps) - The number of amps that the battery can produce at (0 degrees C) for 30 seconds.
RC (Reserve Capacity) - The number of minutes that the battery can deliver 25 amps whilst keeping its voltage above 10.5 volts
Typically, a deep cycle battery will have two or three times the RC of a car battery, but will deliver one-half or three-quarters the CCAs. In addition, a deep cycle battery can withstand several hundred total discharge/recharge cycles, while a car battery is not designed to be totally discharged.
what happens as a battery depletes.
When under load (connected to the pump) the Sulphur reacts with the Lead in the cell and generates electrical current (amps). During this reaction both the positive and negative plates in the battery become coated with Lead Sulphate. As the Current (stored energy) is drawn form the battery the plates become more and more coated. As the process continues the voltage is also decreasing.
Most manufacturers would recommend a battery should not be discharged below 10.5V as the build up of Lead sulphate will at this point cover most of the cell.
This lead sulphate is a soft material and can be separated back into Lead and Sulphuric acid when the battery is recharged.
However excessive depletion of the battery can cause the lead sulphate to harden into crystals on the lead plates. This will mean the cell is less able to hold a charge and will not last as long.
Ultimately over its life this is also why your battery will become less able to hold a charge.
Batteries also discharge via Parasitic discharge when not under load.
All batteries, regardless of their chemistry, will self-discharge. The rate of self-discharge for lead acid batteries depends on the storage or operating temperature. At a temperature of 26 degree C a lead acid battery will self-discharge at a rate of approximately 4% a week. A battery with a 125-amp hour rating would self-discharge at a rate of approximately five amps per week. Keeping this in mind if a 125 AH battery is stored for four months (16 weeks) over winter without being charged, it will loose 80 amps of its 125-amp capacity. It will also have severe sulphation, which causes additional loss of capacity. Keep your batteries charged while not in use!