Set timeout when falling asleep before network disconnects

I'm using OS X Mavericks (latest) on a 15″ 2014 MBP. There's an option to make the system not lock the screen for x number of seconds/minutes after the screen goes dim. I'm looking for an option to not disconnect the network for x number of seconds/minutes after the screen dims.

Here's the situation (happens a couple times a day): I'm VPN'd in somewhere and have a bunch of SSH and RDP sessions open. I then have to go sit in a meeting where I'd be busy talking to someone or looking at a presentation. I try to keep my screen awake but sometimes I catch it a bit late, often right as it's just going totally dark. When that happens I move the mouse and it wakes up and doesn't ask for a password (since it's only been a few seconds) but my VPN has disconnected and all of my SSH and RDP sessions are killed.

Is there any way to set a grace period for when the network goes down the way you can set a grace period for when the system is locked?