Not everything Secretary Clinton did was TS/SCI. The common practice is an Android device[0] that is approved to SECRET only. This would suffice for general email and messaging.

My understanding is that President Obama's blackberry [1] isn't really a mobile device as configured. This blackberry device connects to the a custom secure base station [2] or picocell, that follows him around just like the Football[3], when outside certain vehicles.

Another factor is that TS/SCI access is restricted by location. eg. AF1 or the Presidential vehicle.

I'm not sure the Secretary of State would have a full time [*24/7] detail, although as former First Lady, Sec. Clinton would have a Secret Service detail which is funded separately.

It would be more likely that the NSA offered a different solution and State Dept. bureaucrat balked at the cost involved, especially something like following senior staff around with a football.

[0] http://www.boeing.com/defense/boeing-black/index.page

[1] http://www.technologytell.com/gadgets/156930/yes-president-o...

[2] http://electrospaces.blogspot.com/2013/04/how-obamas-blackbe...

[3] https://en.wikipedia.org/wiki/Nuclear_football

Edit: 24/7 detail at home. On official trips, the Secretary of State would have a security detail as commented by carboncopy below.