o_O, 2 year old thread?
You could have just read the responses in this thread when it gives you the same error for a solution.

I tried to control this

/includes/config.php
$config['MasterServer']['usepconnect'] = 0;

but equal.

I tried to ask my host to increase the connections but it is not possible.

I asked the VB technical support advised me to write here to get a change to the code kindly for not having the constant sending of email for this error.
Can someone help me please?

Why would you need them to change a code for vBulletin? Just go to your Error Logging Options in vBulletin Options (x2) in the acp to fix the settings.

Ignoring the error email does not solve the problem your users are having it only hides it from you.

Each of these error mails is the result of a user trying to visit your board and gets an error page.

Tell your host to increase the "Wait_time" for MySQL