You might miss things like this:

> telomerase activity (the enzyme that repairs the telomeres and lengthens them) increased in both twins in November, which may be related to a significant, stressful family event happening around that time

What a great thought! I was having trouble justifying it myself, so I asked someone else around the lab. They pointed out the very important reason for doing a twin study (as opposed to just following them longitudinally like you're suggesting): you can identify effects that were "going to happen anyway". Sure, we might send them both up and see that they both experienced changes, but we wouldn't know whether this was simply due to genetic predisposition. By comparing the twins side-by-side, the goal is to rule out genetic contributions. Of course, this is difficult with such a small study group, but it represents the start of hopefully a larger set of data.