I've never experienced this issue even across multiple projects over the past 10 months. Sessions on the dashboard always seem to renew properly and only expire if I've not used the dashboard at all for about a week.
I'd suggest making sure that ad-blockers or such aren't interfering. Maybe your browser dev console network tab can shed some light on whether there's anything weird going on.
Even if there was a desktop client (there isn't), sessions would still apply and an expiring session would still cause a logout unless the token was renewed.