The simplest i guess is to try another brand of cornflour/corn starch. Tho I have never had the experience of it going stale or differing by brand.

Some asian cooking uses potato starch for the same thing I think. Its a fine powder too and at asian grocers.

The oldest fallback I guess is to simmer the sauce longer to drive off enough water that it is thick.

Lastly I thought maybe your water there was too acidic or basic and looked it up. Apparently acid may mess with corn starch thickening. Could you try maybe adding some bicarb or other base to lower the PH? This is the link to the place I looked at but I dont know if links will show up here yet... http://www.baking911.com/howto/liquids_thicken.htm

The way you always use corn starch, once you're done, most things tend to simmer, so you mix a bit of corn starch with water to avoid lumps, then add that in and bring it back to a proper boil.
Thing is, where I would usually use a teaspoon or two, I now easily use three times as much, sometimes even more. The thing is, I don't know why.
One suggestion has been the elevation (I'm higher here than I was the places I lived in Europe), but that seems a bit odd, yes, it changes the boiling point, slightly, but the effectiveness of corn starch? Some things are different, like potatoes take longer to cook, be it boiled or baked, they always need more time over here.

I tried flour, even though I don't like the taste it adds, but that's no difference. There's so much corn starch you can actually slightly taste it.

Maybe it's the brand? Fleishmann's or something...
Are there other things I can try using? If so, what?

I assume you are trying to thicken the same volume of sauce, other than that have you tried bringing the sauce mixed with cornflour starch slurry up to boiling again?
I have had sauces that werent hot enough at the time so didnt thicken but once reheated became too thick.