I'd had this before and it always took a reboot of the Slingbox to fix.
Not much use if you're away from home of course, but years of experience with Slingbox has taught me to at the very least put the boxes on a power timer so it reboots overnight, or setup an IP/SMS power switch, and also make sure you have remote access to your router so you can check the Slingbox has been given an IP, make sure port forwarding is still setup etc.
Of course, you shouldn't have to do any of those things but at least it puts you back in control and not so reliant on Sling to fix issues.
Any update on this issue with the 350? Its driving me NUTS. It happens at the LEAST opportune moments and it just annoys me and makes slingbox look bad in front of everyone.
Seriously, ive been following the posts from MONTHS past and still no firmware update for the 350 or any other permanent fix.
Get your act together.