Is it best I just get rid of it and cut my loses?
Not necessarily, but maybe. If your problem is just a leak, then that could be simple and reasonably inexpensive to fix. As VDCdriver suggests, coolant can "disappear" into the engine and that could be serious, but the fact that you can see water on the ground is a hopeful sign.
Do you know if either of your mechanics did a pressure test on the cooling system? If not, then someone should do that. This test is quick and simple, should not be expensive. In fact, a DIYer could do it if you are so inclined or you know someone who might be. It enables you to pressurize the cooling system while the car is stationary, so that you can see if the system holds pressure, and if not, it will cause the leak to appear making it easier to locate.
I’d suggest that you do at least that much and see where the water is coming from. If you want to embark on that test yourself, people here can help you. Some parts stores, Autozone for example, have a tool lending system so you can use their tester and return it for a full refund.
If your mechanics have thrown parts at this without doing the pressure test, then their lack of competence is showing. Given your water leak, they should have known that the fans were not the problem, so you might be better served by a different mechanic. Check the mechanics files at the top of this page, ask anyone you know who might be into cars for a reputable, competent shop. Best to avoid chain auto repair businesses, instead find a locally owned small independent shop…
Good luck, and report back with whatever you find. Also, best to check your coolant level when the engine is cold, and top it up before driving. For now, you might need to do that every day until you solve the problem. What you don’t want to do is run the engine when the cooling system is empty. Then you would have to get rid of the car.