The website reports on the last time data was received by the website via the cell modem. So you’ll have data on the card that’s not on the website. And there are 2 date/time columns in that data file, one is local time (standard) and one is UTC time. They are 5 hours off if you’re in the eastern time zone. So data points in the evening before midnight will have a local time that’s 5 hours behind UTC time, and thus have a date that appears one day behind, but if you look at the timestamp, you’ll see that it’s only 5 hours off.
I can see that your station started transmitting again about 30 minutes ago. Adjusting the panel for good sun is important, but you’ll need to replace the battery with a fully-charged one, or this is going to continue. It’s very hard for the Mayfly to recover from a fully discharged battery by itself while it’s still turned on and operating. You can either turn it off and leave it for a few days or a week and allow the sun to charge it, or charge another battery elsewhere (either using a spare Mayfly or one of the chargers we recommend in the EnviroDIY manual).