leftover nutrient solution

If I mix a large amount of nutrient solution, let's say two gallons, but only use one and a half, can the remaining solution be saved for later use? If so for how long?

Yes, It depends on your nutrients you use but it should last at least until your next watering with nutes. 3-5 days is probably a good estimate. A week on some nutes because theyll stay suspended in the water longer.

I keep mine stored in a cool, dark place and they'll be fine for weeks. I never had any issues with the nutes "dying" off or becoming un-usable.

Dont keep mixed bio-nutes for more than 24 hours or so.

Never mix more than what you need.
If it stinks bad, don't use it.
You can slow down chemical reactions in the solution by storing it in the fridge.

IMO- .50 cents (maybe) it cost to mix up the nutrients. It's not worth saving it.