I think https://github.com/RocketChat/Rocket.Chat.Electron/pull/1800 introduced a bug, that user now can not change status to online
It happens not all time, but in some circumstances

Reload by CTRL+R helps
If user set status to Online it should be online.
If user status become Away because inactivity, then it should set to Online right after some activity (mouse movement or something like that)
Edit: This is also a problem here using Server 3.7.1 and Electron Client 3.0.3. Feels like this could be related to https://github.com/RocketChat/Rocket.Chat/issues/19209
I had the same issue - server considered me "away" and sent emails and notifications to me while I was chatting, I couldn't set me "online".
Resolved by restarting Rocket.Chat and changing the status once again.
Versions 3.0.0 (AppStore) and 3.6.2 server.
I see this in 3.0.5.
Still only CTRL+R helps
3.0.7 issue still here
As I see that issue is server undependent.
Now I get it in open server with 3.10-develop in 3.0.7

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3.0.7 issue still here