Summer is a busy time for us here at EC Miami. We got a lot more students from all over the world looking for US language schools (it is, after all, vacation time!), and it really doesn’t start to die down until the end of August. The number of students that we have here at the school also tends to die down near the end of the year, in December. When the student numbers die down a little, some teachers will take time off; while others will take advantage of the quieter times to to get some long-overdue work done.
Clearly, we’re not talking about people actually dying – that would be too negative a blog post! Die down simply means to reduce in strength (“The wind died down after a few hours”), or to reduce or diminish — such as in the above examples talking about the school and students. Another idiom for your collection!