Why won't 2000w inverter run 900w microwave?

Your problem is simple, the MW is pulling more current than the inverter can deliver and thats causing the MW to shut down. A number of reasons prevail here. wire is too long and the voltage drop is greater than what is needed to run the MW, The batteries cannot deliver the current needed, etc... If the inverter is rated to start the MW and then to continue running it you may need to add more batteries but if it's pulling that much current then you will only have a few minutes at best to run it before you deplete the batteries anyway. This is pretty much why people opt for small generators with at least 3000 watts fo power. you may be able to run your A/C if it's a 13.5k BTU or smaller or the MW but probabaly not both at once. When I tent camped back when I had an actual spine ( Doctors put metal in there now ) I would bnring a 1000 watt inverter to run the coffee pot from home as I HAVE to have my coffee in the morning. That barely brewwed a full pot before the inverter started beeping and the wires got hot. I was going to put 4 12v deep cycles together and use my bohemeth inverters to run everything but the A/C at the rest stops on our long trips but the logistics were too insane. I planned on buying a Honda i3000 but my truck cost me 900.00 to replace all the fluids in the trans, etc. There's always next year! Good Luck and be careful becuase those wires on big projects like that can cause a fire real fast!