Sorry to hear about your birds. Electric fences work well, but only if they are hot.
One additional thing to check is to see if your fence is grounded anywhere. A correctly functioning solar unit will continue working for a long time, but not if it is grounded. That will drain a battery pretty fast. Not only that, but will drain off a lot of zap in the process. So even if you switch to an AC unit, what might be a potent shock might be diminished if the fence is grounding out by a loose wire or something else touching it. A fence voltage tester will help with this. Test the fence at the charger....directly from the hot side to ground side, and again at the terminal end. If the voltage differs much at all, you may have a grounding problem somewhere in your line.
Other things to consider is if you have had an ice storm lately. Since your hot wire is high up off the ground, not likely you have leaves, sticks etc.. My jury is also still out on if snow will bleed juice from a line........in theory it is an insulator........but an ice storm that forms an ice bridge from the wire to a conductor to ground might be enough to drain a solar charged battery.
Yet another consideration........with a single hot wire on top, if an animal climbed the wire fence, their only connection to the ground to close the circuit is through the wire fence. So is the wire fence grounded? If nailed to wooden posts only, you would have to rely upon the wood fence posts to close the circuit to ground, and that may not happen. So if nailed to wooden posts, try tying the woven wire fence to the fencer ground. When you test your line, touch the ground side of your tester to the woven wire fence.
