You need to set your max_user_connections to the number of Apache web server children X 2. This is the absolute minimum and ideally it should be X 4.
DB connections don't consume much resources and having a separate connection for Wordfence gives a substantial performance boost. If your host is stingy on memory for your DB server, find another host.
We don't have any issues regarding max_user_connections with premium hosts.
MickeyRoush is correct that disabling live traffic may help with this. (Thanks for the suggestion!)
Having said that, I do have an urgent issue logged to try and use the WPDB DB handle instead of creating a separate connection. So expect a possible improvement in another release.
Closing this issue because this forum is not a bug tracking system and I've given you a comprehensive response.