You're driving a LED based on voltage, then you're making it worse by using a regulator circuit that is specified at +/- 2.5% regulation. Grumpy Mike would kick your butt for doing it that way. There's nothing about a LED V/I curve that suggests anything but eventual failure.
It's also not necessarily a knock-off/counterfit LM2596 issue. Nat Semi specs their LM2596 at +/- 4% regulation:
Other features include a guaranteed ± 4% tolerance on out-
put voltage under specified input voltage and output load
conditions...