Adapted from a recent online discussion.
Question: I worry that my mother is hiding a health problem. It would be exactly like her to not want to bother me, but when I press her on it, she tells me to stop nagging her and that everything's fine. Anything I can do or say to be sure?
Answer: One thing is certain: If it's a big deal, you will find out eventually.
If you anticipate feeling angry about being kept in the dark, then work to pre-empt your anger now. Specifically, project what you would have done had you known, and start doing some of that now.
Without any information beyond your hunch, you can spend more time with her, you can ask her about family history, and do whatever else makes grieving people say, "I wish I'd had time to X before s/he died."
Now, this may all be a major overreaction; anything could be going on with your mom. However, we've all heard the "live as though you'll die tomorrow" advice, and, while that's not exactly practical, there's a reason it's in the Tacky Kitchen Plaque Hall of Fame: There's no downside to figuring out whether your priorities really reflect what you value most. Don't wait; do this with mom now.
Q: Several years ago I suspected my parents were withholding a health concern. I didn't voice my suspicions, but I did say that if/when there is a concern, I would appreciate it if they gave us kids a heads-up sooner, so we could process it, rather than blindsiding us with dreadful news later. That worked for us.
A: I especially like the integrity of it: If you want people to be open with you about their fears, concerns, and needs, then it can't hurt to start that process by being open yourself about your fears, concerns, and needs.