Can't copy and paste puppet keyframes

Hello! I've recently been learning After Effects, and I've been trying to do puppet animation. However, I've found that keyframes simply won't copy and paste. The undo/redo buttons will even sometimes indicate that the keyframes have been pasted, even though they have never once successfully done so. Is this a glitch, or am I missing something? I've tried CTRL-C and CTRL-V as well as using the Edit menu, and neither work.