Is it possible to "over-train" in samatha meditation? Every morning I set aside one hour for meditation -- primarily just counting breaths, but occasionally abdominal noting. My overall aim is to achieve some kind of basic tranquility so I can then decide if I should move onto something else. That is, I'm doing "samatha meditation" as preparation for "vipassana meditation". (Although I have asked about that apparent dichotomy in another question.)

However, although I reserve a whole hour, at the moment I'm only doing 20 minutes (built up slowly over some weeks from 10 minutes). My current plan is to keep to that gradual build, but sometimes I wonder if I should just "go for broke" and sit for an hour at a time.

One reason I don't is the same reason I wouldn't start out by running for an hour. Instead, I'd start with a shorter period, and build it up. But I don't know if my concern is valid for meditation. There are clear physiological reasons for not building up physical exercise too quickly. Muscles and tendons need time to build strength and flexibility, so even if I felt like running for an hour, I wouldn't. I'd force myself to increase only slowly.

But does the same thing apply for "mental" exercise -- i.e. for Buddhist samatha meditation of the kind I describe? Should I "hold back" even though I'm keen to do more? Is it possible in any way to "injure" oneself by over-training when it comes to meditation.

Note, I'm specifically interested in the mental/spiritual aspects. Im pretty sure it's possible to physically overdo it by, for example, trying to sit in full lotus too long in the early stages (or, in my case, ever).
First, physically, you're probably always going to cause some pain by sitting in a strict posture unless you've been doing it since you were young. So if a person had just started meditation and did so with a great deal of zeal, I could see them causing some pain and stress in the body by doing too much at once. They might even cause some permanent damage if, in their zeal to do it right, they won't sit in anything other than full lotus, even when they're causing pain.

The bigger issue though is that, mentally, there's the danger of getting burned out. Thanissaro mentioned in one of his talks he had friends who would go out into retreat alone for long periods and the problem they would run into is making no progress. Weeks and weeks of no progress in their meditation. It must be tough to become a monk, have one goal, do nothing but practice toward that goal and end up making no progress.

I think it's universal: your practice will have ups and downs. There are times where the mind becomes more and more focused, it lets go of all discursive thought, the precepts become easier to follow, and then there are times when it seems you're sliding backwards.

All in all, the real danger, if there is any, of overtraining is this mental burn out, because when you sink a huge amount of time and energy into something, you want to see short-term progress.

As to whether it would be better to do less sitting than more, I'm not sure. Are you the kind of person who takes on new projects easily and then gives up easily when you encounter difficulty? I suppose the more short-term oriented a person is, the more I'd recommend they just take things slow and steady so that they don't run into a patch of doldrums, get frustrated and give it all up entirely.