So this very well could be a bug with slack but it definitely is websocket related and I don't see it in other browsers. Looking at the console logs (which Slack has in abbundance), after leaving the laptop with display long enough to trigger the "reenter password" state, the websocket isn't able to reconnect (though looking at the console logs it's definitely trying).
I'll need to do a side by side comparision with Firefox or Chrome to compare the log output. For now, I'm upload a text copy of the console logs.