question

It sounds to me like the fuse is overheating or not getting enough ventilation to keep it cool. When a large amount of current flows through a fuse it will warm up, When a large amount of continuous current flows through a fuse it will continue to warm up exponentially if it is not kept cool.
The hotter it gets, the more its resistance increases and so the hotter it gets in a vicious circle. A hot fuse will then have a lower rating than what it would be at ambient temperature.
It's becomes a nightmare.

You did not mention which type of fuse holder you are using or how well cooled it is when its running with such high currents. Are they mounted in a small enclosure?

Some more detail of your setup would be helpful - what voltage battery bank? What type of batteries? How much solar?

Is the solar charge controller wired to pass through the same fuse? If solar is incoming through the same fuse as the inverters then yes that would absolutely increase the current passing through.

A basic schematic of what you have would be very telling to help understand.

Do you have a picture of your fuse holder? I wonder if the heat melted the fuse?

The most common melting problem we find is that the fuse and cable lug are not bolted directly together in the fuse holder, but with a spacer washer in between. The extra resistance from the washer causes excessive heat and possible subsequent melting.

The stainless steel washers commonly used in the marine industry are the worst, the nickel plated brass washers aren't so bad.