Is there a way to directly stream from the software to YouTube?

So I have purchased my 2nd Elgato HD in 6 months. It took me a good while to save for them both hence the gap. They've both had the same problem.

At first, I couldn't get an image to appear on my TV but it would appear on my laptop. Once this was fixed I started streaming via OBS, but after about 5 minutes of recording, regardless of the console or game being recorded, the recording goes into an uncontrollable stutter. The only way to make it stop is to stop the stream and unplug the Elgato device. This happens every time, without fail.

When I contacted the staff behind the device, they ran out of ideas to help me. Please help! I really want to join the speedrunning community with this thing, but can't as long as this stutter issue continues!

(I will try and save a video in the meyantime to show the problem better!)

EDIT: Here is the video, go to 7:10. For some reason there is no sound :O

Hola everyone. I'm planning to run some old PS1 games like Crash Team Racing when I can. Admittedly I feel I'm in over my head - I'm not very bright and have terrible memory so it'll take me a while to pick things up as good as everyone else - but if the community is supportive, I'll give it my best shot!