"Would you like to resubscribe to this broadcaster with Twitch Prime?"
When watching the broadcaster you previously subscribed to with Twitch Prime and your subscription ends, trigger a resubscribe notification In the same way Twitch pops up the "Announce your resub anniversary" notification.
Have it suggest resubscribing with Twitch Prime once it's expired. If they click "share", it automatically resubscribes with their Prime subscription.
Matthew Ward commented
This would be a nifty feature.