Truthfully, I'm more worried about my girls' retirement than my own. Sound foolish? Thing is, my husband and I were able to buy our first house for only 71K, and we had some excellent years in the stock market early in our professional lives. I am in a job with a pension, and I think we will see at least some return on our Social Security payments. Certainly we worked hard, planned and saved . . . But we did have some breaks along the way.
My girls can't really count on these positives. We've taught them frugal ways, we're making it possible for them to finish a bachelors degree without debt, and after graduation we'll continue to give them as much advice and encouragement as they care to hear . . . But they're heading out into a more difficult world than we faced. Also, they aren't out of school yet, so they aren't yet dug into their careers. Perhaps when I see them working professionally, buying houses, saving, etc., perhaps them I'll feel differently.
I doubt your mom was specifically concerned about sewer pipes, but her larger point is that unexpected expenses will always pop up. For example, we've just had a rather large plumbing emergency in our house. Right now my kitchen sink is unusable, and my husband is taking a break and contemplating his next move. She is right to say that you need to have enough saved to cover unforeseen problems.
And inflation. I worry about that.