ASE will only save color swatches, no patterns.
Actually patterns, gradients are supported by the ASE exchange format, This feature is of limited value for Illustrator designers. So you should think about Ai not ASE
I agree with Monika that ASE saves solid color swatches. That's because ASE can be exchanged not only with ai files, but also with InDesign and Photoshop files, neither of which do patterns the same way that Illlustrator does.
When you used the Swatches panel menu to save the pattern swatch as an ai, choosing to open it in another ai file from the Swatches panel menu, should have opened it in a new separate panel with only that pattern. The standard Swatches panel would still have the default swatches.