The actual Sign-up page says this.
As of July 22, 2013, 2 a.m. (PDT), we have temporarily closed the Beta Tester Application Site in preparation for Beta phase 4 (final Beta Test).
The site will reopen once Beta phase 4 begins.
It might be worth trying to apply after Phase 4 begins at 2:00AM CST tonight.
The start of the Phase 4 Beta was pushed up one day for players that meet certain criteria, so that may also effect the time they originally stated sign-ups would resume.