Many dancers have experienced earrings flying off at some point…. and it can happen with both clip-on styles as well as pierced-ear styles.
A handy tip/trick is to put some eyelash glue on your earring (for clip-ons). Yes. Our friend eyelash glue – comes in handy for everything!
(my personal favourite brand is DUO)
For earrings with posts for pierced ears, a common trick is to get a piece of eraser rubber and stick it on the back of the post like a stopper. Similarly, for our larger earrings that have a french-clip backing, we often will include some extra backings as well (not only do they help the earring sit a bit more flat, it really super-secures them to the ear).
Hope that helps!