Error establishing a database connection caused by one particular user

Hello,
I have this very unusual problem.
Very often, when one particular user logs into WordPress and starts creating a new article, whether during the editing or after submitting the post, the website starts to lose connection and then is unaccessible (to everyone) with the message:
“Error establishing a database connection”.
This error only seems to happen with this one particular user.
Any idea??
Thanks!