Ammonia comes from something decomposing and not having enough bacteria to convert it from ammonia to nitrites (and eventually nitrates). The obvious answer could be that a fish died and you can't find it. Ammonia can also come about when people stir up their sand beds and release a bunch of nasties that had previously been locked up in the sand. With how new your tank is, I doubt that's your case.
Another possibility... but there's no way to tell if it's the case... is that you're actually seeing an ammonia spike from some of your beneficial bacteria dieing off. When you got the tank and it was supposedly cycled, if it was truly cycled you would've had a LOT of beneficial bacteria in it because the bioload was so high. Once your fish started dieing, and your bioload dropped drastically, all that bacteria didn't have enough to "eat" anymore. So now that you're fish bioload dropped, your bacterial population will drop. And amazingly... dieing bacteria will cause a shift in water parameters just like anything else will. I'd once read that the bacteria bioload in a tank is actually larger than your fish bioload. (Think I read that in Fenner's "The Conscientious Marine Aquarist". I think.)
Not sure if that's what's going on in your case, but it's just another possibility.
You can add additives (Seachem's Prime, Amquel, etc) that bind up the ammonia into non-toxic compounds, but your test kits will still show ammonia because of how it interacts with the new compounds. You just have to trust it's doing its job. But water changes are the easiest and safest thing to do - especially on a 10g.
Originally Posted by BonnieC
And lastly...dang, if my ammonia can jump that fast (1 is deadly, right?) is there anypoint in keeping a 10g tank? ...
In my opinion, for someone just starting out in the hobby... no. A 10g reef is just not a easy way into this hobby.