The NSA refused to give Clinton a device similar to the one used by Obama: a modified BlackBerry 8830 World Edition with additional cryptography installed. And while Clinton's predecessor Condaleeza Rice had obtained waivers for herself and her staff to use BlackBerry devices, Clinton's staff was told that "use [of the BlackBerry] expanded to an unmanageable number of users from a security perspective, so those waivers were phased out and BlackBerry use was not allowed in her Suite,"[1]
This being Clinton there are probably conspiracy theories (the NSA is out to get her!) but I suspect they simply didn't want to have to deal with it, and had the ability to say no. So they did.
[1] http://arstechnica.com/information-technology/2016/03/nsa-re...