If, like me, you have butter fingers and can't trust yourself to correctly apply glue on tiny pieces without getting it everywhere:
1. Take out an outer x-centre cap (the others don't pop, at least for me).
2. Stuff a tiny ball of Blu Tack into the central hole on the primary plastic part. (The centre cap has a peg that goes in there, but the friction fit is dysfunctional.) Don't push the Blu Tack too far in; it should basically be flush with the edge.
3. Push the centre caps back in.
I've done like 100+ solves and haven't had any centre cap pops since. (I used to get around 1 pop every 3-4 solves, though most often the pops happened during scrambling rather solving.)