Need some quick advice and direction on FPGA uses for quadcopters

FPGAs are volatile devices - they require configuring every time they are powered on. That explains the behaviour you're seeing.

The platform you're using will have some form of non-volatile memory that can be programmed with your code, allowing the FPGA to boot from it every time the board powers up.

There are plenty of small FPGA development boards. Have a look through those listed on Altera's website - they list their own development boards and those made by partner companies. I'm sure you'll be able to find one small enough for use on a quadcopter.

I'd suggest you start by looking at the DE0-nano...

http://www.altera.com/products/devkits/partners/kit-terasic-de0-nano.html (http://www.altera.com/products/devkits/partners/kit-terasic-de0-nano.html)