In my long experience of using Slingboxes the one thing I have concluded is that although they are reliable 99% of the time, there is always the chance of something going wrong, whether is caused by the Slingbox or your router.
At minimum, give yourself remote access to your router so that you can change things like port forwarding, reboot the router so it forces the slingbox to get a new IP address or forces it to setup UPnP port forwarding again.
Also useful, setup a cheap PC on the LAN with remote access so that you can investigate things from inside the LAN (do speed tests, try and reconfigure the slingbox locally etc)
Even better, stick the slingbox on a 24 hour power timer so it reboots overnight.
Optimum solution is to use an IP power switch so that you can power off and on the Slingbox whenever you choose.
This gives you full control with the exception of a hard reset of the Slingbox.
While the intention is that these devices should be setup and left for months and months, and while it may well work as well as that for some, in reality my experience is that at some point you'll need to give things a kick.
I realise that's not going to help your current situation, but it might be worth bearing in mind next time your at the location.
The power supply timer + remote access to your router will likely allow you to solve 99% of your issues without being at home.