In some countries this problem is known from years.
Most of the TV sets in the stand-by mode do not support HDCP. Some of TVs switch their HDCP modules just after entering into the stand-by mode, some of TVs (most of Sony and Panasonic models) switch them off after few minuts.
If the signal on the HDMI output of the set-top box is protected by HDCP the set-top box detects the switched off TV as a non-HDCP-compliant device connected to its HDMI output. Most of the set-top boxes and satellite decoders block all their outputs (YPbPr, SPDIF, SCART,...) when detect such a non-HDCP-compliant device connected. It is why your Slingbox does not receive any signal after switching off the TV.
The simplest solution for this problem is using an active iHDMI cable for connecting your TV. Here is link to such cable: http://ihdmi.eu/cgibin/shop?info=8ihdmi18