Performance Question MySQL

Hello, I have a server with a Mysql Database.

Every time an users logged in, create account, loosing life, .. the server is opening a mysql connection, execute mysqlcommand, close connection.

Now I think this isnt needed and I want to open the mysql connection 1 Time and close the connection only when server is turned off.

So is it a good idea to leave the mysql connection opened? (Does it get timeouts sometimes?) Or is it a better way to connect/disconnect for every command? Same question goes to the Mysql Reader (Ive expected some bugs when dont turn off the reader every time)

Here is my current code: Thanks

public class mysqlconn : MonoBehaviour{
//Define connection (new MySqlConnection)

function 1{open connection, execute, close connection}
function 2{open connection, execute, close connection}

After looking around I found on stackoverflow recommendation to close the connection for effeciency. Google is your friend.