My dad has COPD and his condition is getting worse. How do I ask him to give someone Power of Attorney?

Try the indirect approach. You may want to tell him (and follow through) that you are getting a POA and health directive set up because you know everyone needs one. He may the say, "Oh, we should do this together."

Or he may not but you have planted a seed. You can also point out, in the same detached manner, a story about friends in a mess because they didn't do the paperwork ahead of time - (even a news story will work).

Good luck. This is hard to bring up.
Carol

You could also ask his doctor during your father's next visit to assist you with this concern.You can approach the issue by being caring and asking the doctor what paperwork you should have available in case your father has to go to the ER.
I know it is difficult to watch someone struggle to breathe and will keep you in my prayers.