RE: Anyone local?
I am not even close to you, But.
We have had experience of a lot of charge points, although not the one you have as they are not allowed to be used here.
It is unlikely to be the vehicle as I have seen them work on crap electricity & a consistent problem you are describing would not be in the cars intelligence to develop.
Any issues I have seen are the charge points.
Most common one is a bad connection within the charge unit.
I would suggest opening the charge unit, give all of the connections a very good strong pull and also the lead connections including the trailing socket.
I have seen on some manufacturers units the use of klippon type connectors (which are perfect when used properly) with different size conductors in one connection, which to most engineers and electricians is an obvious No No.
This would mean a connection been made under light load but as the current ramps up a resistance develops causing a shutdown.
However as the company are now saying its not the charge point, I would have said the Charge point test unit the installer used to check the installation after you called them back to check should have shown up this issue.
Sorry I am not able to be of more help, I would say it is a bit of an odd attitude the manufacturer has, as any I have dealt with nearly fall over themselves to see what can be done to remedy any issue as it means they have an answer to remedy any future query from a owner who rings them up or emails them.