Didn't the Xantrex return a specific error code on the front display? Low input voltage (12vdc)? Output overload (120vac)?
Are you sure your batteries are fully charged? 12.6v - 12.7v is a good voltage, assuming you don't have the converter turned on and there's no remaining dynamic charge voltage.
Have you checked current draw of the Keurig using commercial power just to verify it really is drawing its rated ~1450w load? Could be drawing more.
4 ft. long 1 gauge runs should provide less than 2% voltage drop with a 145a DC (1450w AC) load---which should be fine. You may have a bad connection or terminal crimp somewhere causing a large voltage drop. If you have a space heater (or equivalent load), place it on high heat (1200-1400w) and see if the Xantrex will power it. If not, try low heat (600-700w). Either way, check voltage at the battery terminals, then check voltage at the inverter input terminals. Record both voltages. Ideally, you shouldn't have much more than a ~.15v drop with the heater on low, and no more than ~.30v on high. Anything significantly higher indicates a bad connection or terminal crimp somewhere.
Lastly, in reality, the Xantrex is closer to being a 1500w inverter than a 2000w. We owned/used a Xantrex Prowatt 2000 for several years. With loads higher than 1400-1500w it tends to struggle.
Good luck!
