I've just started using the 'system color picker' in AE. It's a great way to build a color palette...until I close my project. Then when I reopen it, my custom colors are gone and I have to build the palette all over again. Is there a way around this?
No. It is what it is - a color picker. Nothing more. If you need to store colors persistently, use the CC Library or respective scripts and plug-ins that have such functions. Nothing wrong with creatively using color controls just to store data in your project...
I absolutely love the Creative Cloud libraries feature. You can keep color palettes across apps organized by whatever project you happen to be working on. I especially enjoy Adobe's Capture app that lets you create color palettes on your smartphone and then, when you get back to your computer, the colors are waiting for you immediately!
That being said, if you have clients who like to make changes all the time, Ray Dynamic Color is a great third-party tool for maintaining a color palette in your project and then easily changing colors across the whole thing.