Unfortunately, this is a common problem, with people sometimes trying for days before they get through. 

The reason is usually a shortage of staff on the booking line, and unfortunately there is no answer other than to keep trying. 

The switchboard or the visitors' centre may be able to tell you what the problem is and how long it is likely to last, but they will not be able to book a visit for you.  Some prisons allow you to book your next visit while you are there or book by e-mail.