The microwave draws from the batteries, so you will be limited by your battery capacity, not your solar (the solar charging is way too slow to keep up). We have 440 amp hours of batteries and our microwave will draw around 200 amps when it's running at full power, so I guess theoretically we could run it an hour on full before hitting 50% on the batteries.
In reality however the big draw on the batteries pulls down the voltage (you'll see it drop big time when you turn it on) so that will cause you to draw below 12V pretty quickly, at least while the microwave is on. This can happen after only a few minutes of use. When you turn off the microwave the voltage will recover, but you'll see below 12 while the machine is running (and if you have auto-gen start on you RV that will cause your genny to start-up). We usually only run it for a few mins at a time.
12 paws, 40 feet and the open road