I am having the exact same issue and it just happened after the most recent web-based slingplayer update a couple weeks ago. It used to work awesome, now, not so much. I thought it could be an Adobe Flash player issue, perhaps using hardware acceleration was the problem. I couldn't directly disable the acceleration with the Sling ActiveX control, but I disabled it by going to the Adobe Flash test site, and right-clicking the control and disabling acceleration. But, no avail. My first clue that it was using the GPU was that my video driver started crashing and the fan was going full tilt. I have an older Dell m1330 with Nvidia 8400M GS. So, it can almost do GPU accelerated HD, but not quite, especially with Flash Player 10.3. My Flash was out of date back to 10.1, but that wasn't the issue. I updated to the latest NVidia Win7 64 Notebook driver, that didn't fix it.
I tried deleting the Flash Player folder in the %Appdata%/adobe folder, but that didn't work. I've also tried uninstalling and re-installing the activex control. What the heck is going on here. This new version of the online Slingplayer is no good for me!!! HELP!
OK, I have just been able to reproduce this behavior. Might be nice if Sling knows about it. When you use the Sling desktop software (2.0.4), close it, then switch to the web player, the web player will no longer display video in Auto or Best/HD, you only see a picture in Best or less. Resetting the Slingbox on the back of the player is the only way I've found to fix the problem. Rebooting it alone did not help. I hope that sheds some light?!