That is your problem! You show a photo of a weak ordinary little 9V battery that probably "falls flat on its face" (its voltage drops very low) when it is overloaded by the high starting current of the pump. Use a much larger battery (six AA or D alkaline cells?).
Also, in my post #9 I mentioned the wrong connection of your capacitor parallel to the 240 ohm resistor on the LM317.
Pin 4 on a 555 resets it when it is at a low voltage. If you connect a discharged capacitor to ground on pin 4 then the 555 is reset during power up, then add a resistor to slowly charge the capacitor and activate the 555 after power up. A 47uF capacitor and 10k resistor will produce a power up reset time of 47uF x 10k= 470ms which is almost half a second.