This sounds similar to a problem I've experienced recently. I teach Webex in our organization so I regularly start a meeting from a PC and then join with my mobile device so I can demonstrate the calling features on a smart phone. Within the last month, the system now randomly moves my Host account to the phone. Because of this I loose the Record function on my PC. I opened a TAC case on this and was told this was by design. Not sure how having the host role reassign randomly can be by design. though. I did ask them to escalate a request to development to prevent this in the future and the tech said he opened an internal feature request for this.
I just opened a feature request for this as well. If you would like to support this request, please click on the link below and vote for it.
https://ciscoccp.ideas.aha.io/ideas/WXCUST-I-11322