Can you go to the log and check the error? You might have to click on the window menu -> Show System console
I run blender from the terminal. I don't know if it is this what you need.
2018-08-23 23:18:03,731 INFO rpr.core_image_cache : CoreImageCache(original): image_size=None, contexts number=0
2018-08-23 23:18:03,731 INFO rpr.core_downscaled_image_cache : CoreImageCache(downscaled): image_size=None, contexts number=0
libc++abi.dylib: terminating with uncaught exception of type FrException: TahoeContext: compile failed //// TAHOEERROR: BVH GPU memory allocation failed
Abort trap: 6
...copying shared history...
...saving history...truncating history files...
I have two eGPU's of which one is the Blackmagic eGPU and it 'works fine' with the other one which is a Vega 64. I say 'works fine' because at the moment RPR for Blender is a bit temperamental to say the least. Blender sees the BM 580 and during renders it plays a part according to my GPU activity monitor. When you say "It doesn't create anything", do you have a black image in your image editor after the render? I have had that happen a few times the past few days, but if I click the red, green and blue colour channel buttons, I actually see the individual RGB channels... just no combined image.
Can you attach the scene so we can test it?
I just want to say that I think my Blackmagic eGPU is working fine with RPR in Blender. I think the issues I've been bumping into aren't related to the BM eGPU. I'm not getting any error messages when I render using the BM eGPU like @allesdings is experiencing. I'll run a few tests later and report any weird behaviour with specific scenes.