It sounds like you're dealing with a form of copy protection from your cable provider called SOC (Selectable Output Control). SOC causes the cable box to stop outputting video to any cables except for the HDMI cable when an HDMI cable is connected. Here is an article that describes SOC (you'll find this information towards the bottom of the article):
Most likely, the reason this is now happening even though it was working before, is that your cable provider updated your cable box with this copy protection.
There are two ways around this:
1) Disconnect the HDMI cable from your cable box (and leave it out), and connect component (red, blue, green, red, white) cables from your cable box to your Slingbox, and from your Slingbox to your TV.
2) If you wish to keep using your TV with HDMI cables, we recommend the use of an HDMI adapter. You can find information on this here:
Hope this helps!