Anyone care to give a ballpark guess as to how long a new Mini-Mac will last until it finally dies, beyond repair.
It may never get to that point. Especially if you have a solid state hard drive (SSD) instead of a rotating disk hard drive. Using a UPS (uninteruptable power supply) is another thing that might help your new Mac to last indefinitely.
The limiting factor(s) will have to do with advancing technology. At some point your Mac won't be upgradeable to the latest versions of the Mac OS. And with that, you won't be able to upgrade your applications anymore. Your Web browser will likely become hopelessly outdated as Web standards advance. Newer versions of your favorite apps (or their successors) will use new and different file formats and won't be backwards compatible.
It's always sad when I hear from a users who has held onto their computer for too long, and they want to know how to translate all of their (relatively) ancient files into a format that is compatible with newer applications. Unfortunately, translators are often available only for a short time, and then the optimal window during which to move to a new file format is gone. For instance, if you were a WriteNow, or AppleWorks user, and you waited too long to get a new Mac and move away from those applications, you may have been too late to find available translators for your old files.
I used to recommend that business users plan to replace their Macs no later than after 5 years, and that home users hold on to them no longer than 7, to avoid technology creep issues. But changes in the economy, and increases in the reliability of personal computers, have home users now routinely keeping the same personal computer for a decade. But after about a decade, technology creep makes it really hard to stick with your old Mac, even if it still runs fine.