Does your server support Forward Secrecy? Run a test against your server at https://www.ssllabs.com/ssltest/ to get an overview.
It is possible to change individual settings and not disable ATS completely.
Diagnostic tool is mentioned here: https://developer.apple.com/library/prerelease/ios/technotes/App-Transport-Security-Technote/
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Ios 9.0.1: $http requests to server that supports TLS v1.2 with valid certificate result in CFNetwork SSLHandshake failed
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