I have checked here and noted that there is sync but haven't seen authentication so can you able to reconfigure modem after hard reset?
please also tell me which modem model/brand you have for your ADSL connection.
There is sync and sync speed is also good in your case as well so that outage is not affecting your service. In modem configuration which encapsulation protocol in use,There are options PPoA and PPoE so make sure it is selected for PPoE. Sometimes that incorrect setting also preventing authentication. If you have spare modem then try with spare one as well.