Mine runs off my 12V network, which in theory shouldn't loose power until the battery bank or the sun dies... Batteries are second hand, dated 2003 and 11 years later it's still pretty good. If only I had a pi back then
What are you using for your weather station? I'm using pywws for my chineese knock off (of a lacrose) + the picaxe data logger I made that does temp and power.