Voltage is dropping, why?

So, you have a 1A supply and want to draw 1,6A?
And a linear regulator that needs to convert the rest (12,8W!!!) to heat?

And you're surprised

And you use Neopixels, not just normal leds. Aka, devil is in the details. Give us schematics, code, type details etc and we can give you useful answers and tips. If you don't, it's just a wild guess.