Hello, Dailong.
That's correct, Round-Robin DNS won't work with WMSAuth because session-id (nimblesessionid) is unique for each server. Each time the chunks are requested, different servers respond to such requests, and 403 returned if the session is not found and access is denied.
If you need a load-balancing solution, please check the following article:
https://blog.wmspanel.com/2015/02/hls-dash-media-streaming-load-balancing.html
Alternatively, you may try using the "absolute_path" option on each server to "stick" the client to the server it started playback from.
https://wmspanel.com/nimble/param#absolute_path
Thank you