Let's put unlimited power in the ledstrip:
Yep, that seems to solve the problem 
calclimb7, the copper traces of the ledstrip itself can not carry all the current. You can attach wires with power (both GND and 5V) every 50 cm or every meter.
I noticed that the picture is taken from the Adafruit Neopixel Überguide. That is a good place to start.