Backup Overload Fault

Can anyone help me with the Backup Overload Fault notification. I've had four today (first time I've had it at all, I'm just a couple of weeks in). I have being using a lot of domestic appliances, peaks load around 6kwh. It seems to switch the solar system off, so I am just drawing from the grid entirely. Couple of times it seems to have then 'fixed' itself when load decreased, but a couple of time I only noticed after around an hour and hit the restart inverter icon which fixed it.
I know there are issues on how much I can use my system as a back up when there is a power cut, but is it going to cut out every time I use a few appliances at the same time?

the back up supply is limited to the inverters maximum output, you do not state which inverter you have so i can not be specific but i expect 2800 watts.
If you want more you would need two inverters but i doubt you can combine the back up outputs so then you would have two lots of 2.3 not 5.6.
others may correct me on this.

Lewis how is your system setup? It’s not designed to take the whole house load through the EPS circuit - it should be on a changeover switch or a separate board that supplies essential limited loads only.
In normal circumstances the load will come from the solar/battery and topped up with grid.

Its a hybrid 5.0. The load used has gone to around 5.7kw before without a problem, but when just over 6kw today which caused the issue. Previously it would draw from the solar/battery (up to 2.5kw) and the top up from the grid as anglefire said.
If the circuit that is set up for EPS (downstairs sockets) went over the max (5kw) would that be the cause?

without solar yes most definitely.

The inverter can be permanently damaged by overloading the EPS, can't it?

Zakalwe I believe it can be if it happens too many times.