For what it's worth, from tvheadend web UI (http://ip:9981) in the debug log, I was able to witness a playback stopped automatically. This is what is displayed. It seems that the connection is lost and then restored. But why...
Code
2021-03-15 21:49:23.772 htsp: Got connection from 127.0.0.1
2021-03-15 21:49:23.773 htsp: 127.0.0.1: Welcomed client software: Kodi Media Center (HTSPv34)
2021-03-15 21:49:23.779 htsp: 127.0.0.1 [ Kodi Media Center ]: Identified as user ''
2021-03-15 21:49:28.782 htsp: 127.0.0.1 [ | Kodi Media Center ]: Disconnected
2021-03-15 21:49:28.782 subscription: 0028: "HTSP" unsubscribing, hostname="127.0.0.1", username="127.0.0.1", client="Kodi Media Center"
2021-03-15 21:49:36.366 htsp: 127.0.0.1 [ | Kodi Media Center ]: Disconnected
2021-03-15 21:49:36.366 htsp: 127.0.0.1 [ | Kodi Media Center ]: Write error -- Broken pipe
2021-03-15 21:49:36.366 subscription: 0027: "HTSP" unsubscribing, hostname="127.0.0.1", username="127.0.0.1", client="Kodi Media Center"
2021-03-15 21:49:43.791 htsp: Got connection from 127.0.0.1
2021-03-15 21:49:43.792 htsp: 127.0.0.1: Welcomed client software: Kodi Media Center (HTSPv34)
2021-03-15 21:49:43.793 htsp: 127.0.0.1 [ Kodi Media Center ]: Identified as user ''
2021-03-15 21:49:43.988 dvr: "Le bon docteur" on "TVA": Updated ()
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Full tvheadend log here: http://sprunge.us/CqEdeV