YouTube: The API server failed to successfully process the request.

This is a general error that YouTube may return for some actions, but most often the user may see the following variant of the error when trying to send a reply from the service:
The API server failed to successfully process the request. While this can be a transient error? it usually indicates that the request's input is invalid.

As can be understood from the error text, it is temporary in nature and relates to occasional failures on YouTube's side.
As a rule, the reply can be successfully sent after some time.