Why do actors have issues with booking out with their agents? Actors that book out are really doing themselves a favor.
Think of it this way. If you were an agent and had several choices of who to call when you needed an actor, all other factors being equal, who would you go to first? The choices that are reliably available or the choices that may or may not be available. By reliably available, I do not mean available 364 days/year no matter what. I mean you know 99% of the time that you are not going to be wasting time contacting unavailable actors. The 1% is to allow for extenuating circumstances such as medical emergencies.
What is the proper way to book out? Depends on your agent, but most likely email, perhaps a phone call. Even without taking a survey, I feel confident in stating that no agent approves of a Twitter post or a Facebook update as a proper way to book out. Too easy to miss, assuming the agent even follows you in the first place.
Remember, consistently being unavailable is not a good thing either. Even if you religiously book out. Of course, if you are consistently unavailable because you are consistently on set that is an entirely different matter. Agents like representing actors who are consistently on set.