If the connection times out, it won't work.
To answer the question from the comment, to cope with the problem, refer to php.net manual page for mysql_connect() which says:
If a second call is made to mysql_connect() with the same arguments, no new link will be established, but instead, the link identifier of the already opened link will be returned.
so if you want to make sure you always have an open connection, just try to open a new one with the same arguments after the code you substituted with sleep() is done executing.