How long does gelatinized broth keep?

i read somewhere that if it is not used in 3 days, reboil it and then back to fridge, but then use in a day or so. i've used that theory or rule for decades and the broth/stock has remained good.

If it's gelatinized, congratulations, it means you've made your stock properly. Under a week in the refrigerator is fine (40 f or less). Beyond that it should go in the freezer.

Assuming you've kept the broth in the refrigerator, it should be okay. It won't be as fresh as the day you made it, but it'll be edible.

I've kept stock in my fridge for about a week or so many times before and I always notice a decline in the stock's freshness over time. If you're not going to use it in 2-3 days, it's best to freeze it.

My general policy is keep things in my freezer no longer than three months, but stock will last longer than that in the freezer. My freezer policy is mostly for inventory control and not accumulating too much stuff.