I like to keep my agave in the fridge. You can also keep in the the cabinet but it can taste slightly less fresh. It stays liquid in the refrigerator so that’s the best bet. I’ve kept raw agave and the non-raw maple syrup refrigerated for weeks, sometimes even a month or more, and it still stays fresh. Just be sure you’ve got it airtight.
I haven’t ever refrigerated it. I get gallon jugs and pour into a smaller bottle to keep on the counter. We go through a gallon every couple of months. I’ve been doing it this way for 2+ years and never noticed a difference in taste or freshness.
Plus, DH is a little sloppy, and it’s easier to keep the counter clean than to face all that stickiness in the fridge.