This is your lucky day. West Marine has a table of
Marine Wire which shows wire gauge vs length and current. It's on page 422.
For a 1000 watt inverter, you're drawing about 80 amps (1000 watts/12.5 volts=80 amps) and your total distance is twice the wire length. Remember the current has to get there from the battery and then return. When I installed a 1000 watt inverter in Journey On, it was a 25' run from the battery to the inverter, so make sure you measure the run accurately. I used 25' of 4 gauge to and 25' of black back. Works well.
I hope you have a true sine wave inverter, everything works so well, as opposed to the square wave.
For the wire, I did an internet search to buy it. At the moment West Marine wants $3/ft for the tinned stuff. Since you're using the inverter in a closed boat, you can consider non-tinned wire. I crimped the lugs with an Anchor heavy cable crimping tool, P/N 701010. They're expensive at West Marine, so another internet search would be good. I also sweat soldered the connections, but that's not necessary.
Remember, smaller wire will just spend your battery energy in heat, so get the right size. That's why your inverter is shutting down: low voltage.
Boris