WP DB Error max_user_connections

I’m currently getting this error in the front-end only (not inside /wp-admin):

Warning: mysqli_real_connect(): (HY000/1203): User xxx already has more than
'max_user_connections' active connections in
/hermes/.../public_html/myhome/wp-includes/wp-db.php on line 1489

Warning: mysql_connect(): User xxx already has more than
'max_user_connections' active connections in
/hermes/.../public_html/myhome/wp-includes/wp-db.php on line 1515

Error establishing a database connection

And I’m wondering how come the max connection error appear when I’m the only visitor? I’m using WP 4.5. I checked the 4.5 known errors. I found similar errors but not exactly the same. When I changed the theme from Nimva to Twenty Fifteen everything works smoothly.

I did contact the host who says:

There are two cases the script loads
above error, one is when there is a
high traffic to the website and
database concurrent connection hits
the limit and second case is the
database connection is not closed in
the script, even for the moderate
traffic the script loads concurrent
connection error. To overcome this
issue, you have to close the database
connection immediately after
fetching the required content from
the database. To close the database
connection you can use
mysql_close() PHP function with
connection parameter. This will help
you to use database connection limit
efficiently.

In other words, everything is fine at our end, it’s a WP error. It is a WP error since resetting the theme to something default resolves the issue.

How to find and fix the error? I tried debug bar but of no help.