> How can I update Arch, on a semi-regular basis (at least yearly)
You can - in fact, it's best to do it more often than yearly.
> without having to worry about upgrade issues?
Compared to someone who's coming from Ubuntu, Arch isn't a distro that you can just upgrade all in one go, without thinking twice, and then forget about it. Or, to quote the Arch Wiki, pacman is not a 'fire and forget' package manager.
If your definition of 'stability' is 'I can run a full system upgrade as often as I want, without thinking about what I'm doing', then no, Arch isn't 'stable'.
If your definition of 'stability' is 'My system will run with minimal errors and above-average security as long as I carefully consider each package before I update it', then Arch is incredibly stable.
The concept of stability, in the context of a personal user, comes with an implicit assumption of how much choice will be presented to the user, which affects how much mental effort the user will have to provide. Ubuntu will make a set of choices on behalf of the user, which can result in bloated software packages, serious security concerns and bugs that persist for the six-month release cycle or longer. Arch will require the user to make some of those choices for himself or herself, which ends up by providing the user with a more modular set of packages, a much faster upgrade cycle, and a more (easily) configurable system.
For example, there was a bug in X that affected pretty much every distro a few weeks ago, allowing the screen lock to be bypassed trivially. If I remember correctly, Arch had that fixed within a few hours (the advantages of rolling-release). I'm not sure when (or even if) Ubuntu fixed that bug, but it ends up taking much longer, because they have to provide official support for those packages, and something as widespread as X needs to be tested against a variety of configurations before releasing a patch. With Arch, I can decide if the patch is important enough to update now, or if I should wait, and I can make a reasonable judgement as to whether it s compatible with my system -- something Ubuntu users will have a harder time doing, because they didn't go through the process of building their operating system from scratch when they installed it, so they may not understand it under the surface as well.
To put it another way, using a rolling-release system like Arch is no less stable than a fixed-release cycle, because nobody is forcing you to upgrade a package when it comes out.
(The other difference is that Arch provides community support, whereas Ubuntu provides corporate support, but at that point you're starting to compare apples and oranges).