Sounds like standard reconnect every 24h, many ISPs do that. reset your modem at a weird time to get the interruption at that weird time in the future.
I think the OP is so eager to get back online he sees 3:40 every day and is using that timepoint as his troubleshooting clue.
However If he were to disconnect 3:10 and then just be offline an hour until plugging the device back he would probably see the reset happen 4:10 going forward.
