Edit 2016-01-03: The renewed certificate for s3.amazonaws.com uses the SHA256 algorithm and complies with ATS requirements.
Original answer: s3.amazonaws.com uses a SHA1 cerificate that does not meet ATS requirements, resulting in a hard failure. Per the App Transport Security Technote, ATS in iOS9 has the following requirements:
The server must support at least Transport Layer Security (TLS) protocol version 1.2.
Connection ciphers are limited to those that provide forward secrecy, namely,
TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384
TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256
TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA
TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384
TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256
TLS_ECDHE_RSA_WITH_AES_128_CBC_SHACertificates must be signed using a SHA256 or better signature hash algorithm, with either a 2048 bit or greater RSA key or a 256 bit or greater Elliptic-Curve (ECC) key.
Invalid certificates result in a hard failure and no connection.
SSL Labs’ SSL server test (https://www.ssllabs.com/ssltest/analyze.html?d=s3.amazonaws.com) includes a handshake simulation for ATS in iOS 9 that indicates a failure for s3.amazonaws.com.