Yesterday, I was browsing through some forums and came across a relatively common theme; "seahorses don't do much", "seahorses are sedentary", "seahorses are boring". Au contraire! Another vast misconception. In my experience, if seahorses are acting in this manner than they are trying to tell you that something is amiss. That's not to say that they should be dashing around the tank constantly like Dory on speed, but to describe them in this manner is a little inaccurate. Seahorses are a naturally inquisitive, active, playful creature and can often be found circulating the tank looking for prey (or flirting with each other, of course!).
Any seahorses that pretty much sit in one spot all the time most likely have an issue with the environment they are in; flow to high, tank mates causing stress, water conditions off kilter or in the worse case, illness.
If a seahorse is not truly captive bred they may not be used to life behind glass, so this can also be a cause of stress.