I was at the UK Maker Faire in Newcastle as the weekend and nearly got my OpenROV working. All the thruster were working out of the water, not perfectly but spinning in both directions but when put in the pool as soon as the vertical thruster was turned on then I lost power and could only get it going again by taking the batteries out and back in.
Ensure the basics are in place. That the ESCs are both programmed and calibrated. It sounds like you are pulling too much current for the batteries. Are you using standard C batteries? I have run C's successfully underwater so it can be done. Please note that you can you can use 1,2,3,4,5 to change the max throttle of the keyboard to 20%,40%,60%,80%,100%. If I recall, it defaults to 40% power.
I’m using the latest recommended rechargeable batteries, do I need to use the latest Arduino and cockpit code as I’m using the default from the downloadable image file