The only issue I've run into has been with my attempt to reuse the same AsyncClient to make multiple concurrent requests to the same remote host. It looks like this issue may have been fixed in 0.10 or 0.11 so I'll be upgrading soon to check.
Also, be sure to check out the other fantastic projects by Encode. https://github.com/encode I stumbled upon httpx after using Starlette and Uvicorn for one of our microservices and and been pleasantly surprised by how easy to set up and use they are.