Too bad you can't put a Radioisotope Thermoelectric Generators (RTG) up there, I here they worked great for lighthouses in the arctic. There were approximately 1,000 in the soviet union whats now Russia, most of which were used as power sources for lighthouses, navigation beacons and radio repeaters. As a bonus you cold keep your coffee or tea warm on them. I believe they all got replaced (well the ones they could find) with solar and battery storage so if they can get solar and batteries to power a light house in the arctic it should be possible here.
In all seriousness it would be easy to power that repeater off solar and storage, I'd drag an actual solar guy up there to have a look at whats wrong, my guess is the battery is way under sized.
I believe there are several remote radio sites around here in remote Oregon powered off solar and batteries alone.
One I visited a few years back had something like a 5kW array and a 25kWH battery. (I think thats sized for a month of load no sun at all)