PHP-MySQLi connection randomly fails with "Cannot assign requested address"

I had this problem and solved it using persistent connection mode, which can be activated in mysqli by pre-fixing the database hostname with a 'p:'

$link = mysqli_connect('p:localhost', 'fake_user', 'my_password', 'my_db');

From: http://php.net/manual/en/mysqli.persistconns.php :

The idea behind persistent connections is that a connection between a client process and a database can be reused by a client process, rather than being created and destroyed multiple times. This reduces the overhead of creating fresh connections every time one is required, as unused connections are cached and ready to be reused. ...

To open a persistent connection you must prepend p: to the hostname when connecting.

MySQL: Using giant number of connections

What are dangers of frequent connects ?
It works well, with exception of some extreme cases. If you get hundreds of connects per second from the same box you may get into running out of local port numbers. The way to fix it could be - decrease "/proc/sys/net/ipv4/tcp_fin_timeout" on linux (this breaks TCP/IP standard but you might not care in your local network), increase "/proc/sys/net/ipv4/ip_local_port_range" on the client. Other OS have similar settings. You also may use more web boxes or multiple IP for your same database host to work around this problem. I've realy seen this in production.

Some background about this problem:
TCP/IP connection is identified by localip:localport remoteip:remote port. We have MySQL IP and Port as well as client IP fixed in this case so we can only vary local port which has finite range. Note even after you close connection TCP/IP stack has to keep the port reserved for some time, this is where tcp_fin_timeout comes from.