I wonder if anyone else has issues keeping their solar charger going in December around here - I have to swap out batteries every other day to keep ours running right now. I put the "spare" on a trickle charger in the shop to get it back up to par, then swap them out.
Since this is the charger that is ONLY on the two stallion pens, it's got to work - when it goes down, the two brats have way too much fun playing bite-the-chin and will take down the no-climb if not stopped. We went to a solar charger for the studs after a few winters of lengthy power outages and one scary injury over a not-hot fence. It seems self-defeating if it can't keep up enough charge when our northern midwinter days are so stupid short, though. We are way north in WA state.
I'm in the Northeast and have never had a problem with my charger like you describe. Is it new? Was it properly charged initially? Maybe both batteries are defective, or the charger? Is there a "hot line" to the mfg you can call, or a place to have batteries and charger checked? Hope you can resolve the problem soon.
Sounds like the batteries are worn out, or not of sufficient capacity. A fully charged battery should last longer than a day. Look at the battery you have (size and amp-hour rating) and find another with more amp-hours. They're probably gel rechargeable, which are very replaceable. I found one for my burlar alarm on ebay for $17, new, including shipping. Other prices ranged $43 - 140, so be selective.
Also, I'm assuming you have an appropriate solar setup. I wasted my money on four chargers until I finally figured out that I had to buy a reasonable surface area array and a 12-volt system. If you're using less than 12 volts, and/or less than 2 ft^2 of array, it just won't work. Biggest 12v Parmak has worked well for us.
I am in the same state as you are. I have the Parmak 6V solar charger and have not had any issues w/retaining charge in the winter. I did, after about 4-5 years, have to purchase a new battery for my charger but beyond that have not had any issues.
I do live in a much drier climate than you do so my charger does not have to work through lots of tall wet weeds. We also have lots of clear days (albeit cold!) that are good for recharging the battery.
Is your solar panel in a south-facing location that is clear of lots of trees and/or buildings?