I just had this problem too. It may sound funny, but check you plug connection. I saw some message here where people where having trouble with thei plugs and were buying new ones. I remember around the time the lights started blinking, I plugged in something else to the plug outlet where I have the slingbox plugged in. When I removed it, and unplugged and re-plugged in the slingbox the light stopped bllinking. It may be coincidence, but could be worth a shot.
If you already check the connections with the power supply and you are still experiencing issues with the network light of your Slingbox, try the following link:
Here you will find additional troubleshooting steps that can help you on this situation.