sounds awfully similar to what i used to have on my Taffeta White Accord - no amount of washes can get rid of them but if you take a
clay bar to it, you'll notice that they lift right off. i still cannot find the cause for it except to assume that it was the (coincidentally)
Fusso Coat 12 Months Wax Light Color that i used and that the road grime somehow bonds to it.
other than that variable, i cannot think of anything else and unfortunately (or fortunately) i didn't kept that car long enough to ascertain whether it was the wax or not. however you can try for yourself and see.
if the stains can be removed via a claybar then you remove a small portion of it but enough to make 2 parts, one being the part without the wax and the other with the wax applied. leave it for 3 to 5 months and then see the difference.
the liquid should be some sort of cleaner (IPA or alkaline based solution) which generally would remove most stains but at the same time strip almost all LSP on car paints so if you pour water over the part that has been wiped, you should notice that water no longer beads and also it sheets on it.
with ceramic coatings now becoming very affordable, it is a good long term investment for your car. all other superficial claims aside but it definitely makes car washes a heck a lot less tedious.
I suspect it's the fusso coat too. Sometimes I feel it's "sticky", I could even put my fingerprints on my car body. It's the 12m in a can thing except I bought the darker coat one. Next week I will have appointment with the detailer for him to remove it. After that I will not put fusso coat to test.