Yeah, you must be feeding the slingbox from your TV. He's right you should try to turn on the box when its off. I'd also test it by bypassing your tv by feeding the cable box to the slingbox.
1 thing also comes to mind -in my case - possibly your issue is- When I use my Apple TV, stop using it- turn the TV off, the Apple TV seems to sleep and when I turn my tv back on it gives me a "blue screen on my tv and it then starts up again. Is it my tv that stops taking the hdmi feed or is it the box? Don't care enough to check but it may be your issue.
If I were you I'd try the s-video + red white audio into the slingbox straight from the box. I do this and I'm able to use the HDMI from the box and the s + red white at the same time.
Also - My cable box came with a universal type remote that has 2 power buttons. One for on/off of multiple things (TV, Receiver) and one that is a single power button. Is your blaster is turning a couple of things at the same time maybe? Did you have your IR blaster "learn" from your remote?
If all else fails pull the plugs and reset everything. By the time I ever get to that point (a few hours in) I always wonder why I didn't reset everything in the first place. Never fails. There is always a sense of defeat but time is so much cooler than defeat. I would have usually saved myself more time posting and searching.
geez - Sorry about my SirLongWindAlot -