The polling heartbeat's pending-update probe treated a stopped updater
(running=False) as "someone else's job" and silently reset its counter,
so a long-poll task that disappears with no reconnect in flight was never
recovered. get_me() on the general request path stays healthy, so neither
PTB's error_callback nor the connectivity probe ever fires — the gateway
keeps running but stops receiving messages indefinitely (#55769).
Detect the stopped-updater case directly in _probe_pending_updates and feed
it into the existing _handle_polling_network_error ladder, debounced over two
consecutive probes so a just-starting updater or the brief stop()->start_polling()
window of an in-flight reconnect never trips it.
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