Why does my 2000 watt inverter not operate my microwave?

my microwave is 1200 watts but when i turn it on the inverter reads it is using 2300 watts. i turn the power down to 50% and it then reads 1250 watts but will operate for about 6-7 minutes before it shuts itself off. it will restart again after about 5 minutes. is the inverter faulty? its supposed to have a 4000... show more my microwave is 1200 watts but when i turn it on the inverter reads it is using 2300 watts. i turn the power down to 50% and it then reads 1250 watts but will operate for about 6-7 minutes before it shuts itself off. it will restart again after about 5 minutes. is the inverter faulty? its supposed to have a 4000 watt peak and is almost new. it is installed in a semi truck, 2012 model with hook ups for an inverter.
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