urgent prestashop website error work

Hello, we have our own dedicated server, where we have 3 different prestashop sites installed and running. however one of our site now, which receives moderate traffic, keeps giving error:- Warning: mysql_connect(): max_user_connections' active connections............Link to database cannot be established. We contacted our hosting company where our server is, and they said possibly due :Script timed out before returning headers and too many running processes where the processes are not being closed properly We need someone skilled who can solve this issue properly the way it should be done. we need to get this done very urgently, and fixed within 1 day as our site is down