Battery will not hold a charged

Unfortunately it sounds like the battery just won't hold a charge any longer. The way to tell this is to load test the battery. Most parts stores can do this free of charge.

https://www.2carpros.com/articles/car-battery-load-test

Unfortunately the alternator is not designed to recharge the battery. They are only meant to maintain proper operating voltage. So if a battery is 12.6 volts, an alternator charging 14.6 volts will just maintain the battery around 12 and a half volts. So if the battery is around 11 volts, it may bring it up to 11.5 volts or even close to 12 for a short time but the battery is damaged and will not stay there. Hence the reason it worked once and then drained again.

Sounds like you are going to need a new battery but let's have it tested just to be sure. If it comes back as needing charged, you will need to use a battery charger as running the engine will not charge it enough as you have found out.

Let us know what happens. Thanks