- The only way I can think of, that this would happen, is if you are connecting the pump to the NC contacts of the relay.
- When the Arduino resets, the pin connected to the MOSFET defaults to an input, so it does not output HIGH, and so the MOSFET switches off because the 10K pull-down resistor pulls it's gate to ground. This cuts off the current to the relay coil and the spring inside the relay opens the contacts (meaning the common contact touches the NC contact, not the NO contact).
I noticed in the schematic that there is an led indicator driven by the relay's second pair of contacts. Please describe when you see this led switch on and off when the reset behaviour occurs.