PHP and MYSQL servers that are shutting down.

I have a header file with the connection settings to the mysql server.

$link = mysql_connect("localhost", "<username>", "<password>")
   or die("Could not connect : " . mysql_error());

mysql_select_db("<databas_ename>") or die("Could not select database");


i do an include("databasehead.php"); which contains the aboved code..and only that.

I setup my page for queries....

then at the end i close it with a mysql_free($result);
and a mysql_close($link);

my question is: the server, sometimes under heavy traffic, the query will fail, and it will or loose the connection or the server will shutdown.

Why would a server do that?

is there something wrong with the code?
Is there ways to prevent this?
Also because of the fact that i am using the $link inside another file...THAT $link in the mysql close is not the same one..hence its not even closing it? and ...if not..how can i make it so that it will correspond to the same one?

Also....If i open a connection and close it on EACH web page is it a smart idea? or a bad idea?
Reason i am asking this is that I dunnot know where the person will click from, and its not neccessary that it will be comming in from the front page hence if they came in from  soemwhere it would load the stuff from the database.

If i dont close the mysql_close connection is that bad? Will it just time out? do nothing?

because if i can not worry about the close but concentrate more on reducing the amount of connections then maybe its better?