Arduino Uno USB-serial handling is very bad. We recommend to use a teensy instead. If some data are being lost in the USB communication we can't guarantee it will work, and with Arduino’s it's complicated because there are several models / manufacturers which are putting different USB chips.

Teensy is 15$ and can handle very high speed on many LEDs.

Although the best solution is to get a LED driver like Advatek Pixelite.