Unfortunately the seats get taken up as soon as it opens up because students want to take the test early as possible for the upcoming cycle. There are only certain amount of seats per testing center per certain region of the country.
Your best chance is to keep checking them regularly everyday throughout the day. Have your laptop with you everywhere you go and just randomly check for seats. I assuming many students register for the May and June test thinking they will be ready by then, then they realize school work, job, volunteering obligation, etc...gets in the way of their studying and end up dropping because they are not ready to take it. You just have to be lucky enough to be there to grab the seat.
It's not impossible to grab a seat for May and June because people I know have been able to register near the test date as seats open up when people drop.