Running Washing Machine from an Inverter
That sounds like either:


A load regulation problem on the inverter interacting with an under-voltage protection in the washing machine. 
A load regulation problem on the inverter interacting with an over-voltage protection in the washing machine. 


If the machine “tries” to start but it fails, it is the former (the most likely scenario). If it does not even “try” it’s the later. 

Adding a load either reduces the inverter voltage, or makes the washing machine a much smaller proportion of the overall load. A motor initial current transient can be quite significant and the inverter might not be able to handle it fast enough. 

Check the specifications on the inverter. There are such things as passive ferroresonant AC voltage regulators, but I doubt you would find one that would handle the WM load. You might want to keep an electric space heater handy by the WM. 

Electronics age as they are powered, but there has been a long argument regarding how much more aging is done by the initial power-up stresses.