What causes the “max_user_connections” warning on WordPress frontend?

Not WordPress related, so I am not sure if I have the right to reply in here, but still increase max_user_connections in my.cnf MySQL configuration file since you are just testing.

There are number of causes for running out of connections, the most common ones involving when the Web/App server is creating unexpectedly large numbers of connections due to a miss-configuration or some script leaking connections or creating too many connections in error.

The solution: Some people increase max_connections to some very high number so MySQL never runs out of connections.

This however can cause resource utilization problems eating memory and cause MySQL server to swap or be killed by OOM killer process or very poor performance due to high contention.