Or even a 6V accumulator with a LDO 5V regulator to power the Arduino. So 6V at 40mA if repellers are off, 440mA if on. Use a logic-level MOSFET perhaps to switch the repellers on/off. If using battery power you can sense the battery voltage via a resistor-divider to detect when its going flat (lead acid batteries are completely intolerant of over-discharge and will be wrecked if you let this happen).
If you know the proportion of time the repellers will be on it means you can estimate the average current drain and get a good estimate of
the battery capacity needed. Lets say "50% of the time" and you want it to run for 1 week, thats 168 hours at 0.24A, or about 40Ah. Since batteries lose capacity with age you'd then double that to 80Ah for a realistic value. 6V 80Ah is about the size of a car battery.
If the repeller is only going to be on for a small percentage of the time it will be worth going to a bare-bones Arduino and using sleep-mode
to reduce the average current and get more battery life per unit-capacity.