That floating input may be a problem.
I don't know what regulator is used on the mini, but 6V may not be enough to reliably get regulated 5V out. I know that the 78xx series needs 2V - e.g. is you have a 7805, you need to put 7V in to get 5V out.
Not really clear on what the 7806 on the GSE side is for; if it's for the arduino input, then it should be a 7805 as the ATmega requires inputs to be at Vcc (IIRC it's Vcc + 0.5V, but either way 6 > 5.5).
Also, the program will run the loop again. From a reliability and safety standpoint, I'd make the code one-shot - add a while (1) {;} infinite loop at the bottom of the if block (after "close valve") so that a bad input (noise, or that floating input from the no-longer connected GSE) doesn't try and make the sequence run again.
-j