I use Ctek battery charger maintainers on everything. I just had to replace the battery on my riding mower, and took the old one in for exchange and learned that I had it for five years. I have the maintainers on the mower, my big generator, the wife's car and my diesel truck with two batteries. Batteries will still go bad but they last much longer when a maintainer is used. On the car and truck they are installed under the hood and I have an extension cord exiting through the grill so they are plugged in nightlyUnless you run your generator often, your battery will lose power just sitting waiting for an emergence to happen.
I use this... Automatic Battery Float Charger
I use one on my riding mower, and on my car, been doing that for around 7 yrs now, works very well.
It only maintains the charge in the battery, it doesn't charge it. So it needs to be plugged in all the time.
They usually go on sale for $5, I bought a few of them in case one burns out.
Let us know when you get the generator/starter working.