I don't have any Logia equipment. It looks to me they are rebranding some else's product.
Most likely your system has a solar panel proving power during the daytime hours. The solar panel is probably also supposed to recharge a capacitor to provide power in darkness. My guess is the capacitor or associated circuitry may have a problem.
My first choice would be to contact Logia Support:
https://logiaweatherstations.com/pages/contact-us. . . and see what they say. I wouldn't be surprised if they don't have a practical solution (other than to buy another product), but you have nothing to lose by trying.
If you get no satisfaction there is
some possibility that you might be able to diagnose/replace the capacitor yourself if you are willing to experiment at the risk of further damaging the unit. But first see what Logia says.
One option that might fit your situation would be to leave the failed capacitor in place and just provide "wired" power to the unit (essentially bypassing the batteries).