If there were absolutely no losses and everything was perfect, 135WH should be able to power a single v4 for approx 50-75 hours (keep in mind your calculation is 1 amp at 12 volts and the cam only runs at 5 and uses around 0.25 to 0.5 amps). We know there are losses, especially in the conversion from DC to AC so it will be lower than that. But seems like it should be able to handle more than a day especially when the cam is idle most of the time.
Of course the question becomes is it actually charging the battery properly and in a timely fashion. Batteries, especially lead acid (if that’s what this is) charge slower as they get more full.
I’m not sure what kind of battery it is (USB battery bank maybe?). If it is a full on solar setup with rectifier, charge controller, etc, may as well just toss a big deep cycle battery on it. Given that it is a 100W panel I’m guessing it may be that sort of setup, that’s not something I’d expect to find powering a USB output.