Vb.net to sql Server connection

I have a winForms application that is doing tons of reads/writes to a database on hundreds of installed clients.    My question is ->  Is it better to open a connection to the server and keep it open during the session (hours - sometimes days).

(One issue here is that if computer goes to sleep after inactivity SQL will drop the SSID.)

OR

is it beneficial to Open/Close connection on every read/write.   This would be cause some additional overhead.  But, would always ensure that a new connection is established (if server is available).

What is your experience?