If the Chat connection is idle or disconnected, the Chat will be ended in 40 seconds. To increase this idle connection time out, use Idle Connection Warning Duration and Idle Connection Timeout Duration.
Idle Connection Warning Duration
40 seconds plus the value entered in this field before warning is sent.
Idle Connection Timeout Duration
40 seconds plus the value entered in this field before chat is timed out.
Video Reference:
SOQL to check:
SELECT Detail, Type, Time
FROM LiveChatTranscriptEvent
WHERE LiveChatTranscriptId = '5705Y000008358iQAA'
ORDER BY Time ASC
Idle Connection Warning: