I have the Elgato HD and it gets confused by the RGB to component converter. Once you plug in component cables it's looking for something higher quality than 240p and can't pick it up.
Just like a % of modern LCD TVs, the video input modules demand a genuine 480i signal or better in the green Luma/Y jack when using YPbPr/Component or they will reject the signal. They will still accept 240p in S-Video or Composite jacks, though. You would need a
resolution doubler (AKA upscaler) to make it 480p to work in those cases or another model that supports 240p in the first place...
Luckily, I bought one that does accept 240p when using YPbPr/Component. The
F03147 HD USB 2.0 Video Audio Capture Grabber - I made a note of it here for my SNES YPbPr mod thread. Fully tested, confirmed to work as I have SNES screenshots from it via YPbPr (added one below).

