aws-sdk-php: Consecutive API calls return curl error code 35 on CentOS 6.5

After initializing the S3Client with just a key and secret, I can only make 1 API call before getting curl error code 35.

E.g.

$s3->putObject([
    'Bucket'=>'MyBucket',
    'Key'=>'MyFolder/',
    'Body'=>'',
    'ContentLength'=>0
]);

The 2nd time results in the following error:

PHP Fatal error:  Uncaught exception 'Guzzle\Http\Exception\CurlException' with message '[curl] 35:  [url] https://s3.amazonaws.com/MyBucket/MyFolder/' in /home/mike/src/awstest/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php:338
Stack trace:
#0 /home/mike/src/awstest/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(279): Guzzle\Http\Curl\CurlMulti->isCurlException(Object(Guzzle\Http\Message\EntityEnclosingRequest), Object(Guzzle\Http\Curl\CurlHandle), Array)
#1 /home/mike/src/awstest/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(244): Guzzle\Http\Curl\CurlMulti->processResponse(Object(Guzzle\Http\Message\EntityEnclosingRequest), Object(Guzzle\Http\Curl\CurlHandle), Array)
#2 /home/mike/src/awstest/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(227): Guzzle\Http\Curl\CurlMulti->processMessages()
#3 /home/mike/src/awstest/vendor/guzzle/guzzle/src/Guzzle/Http/Curl/CurlMulti.php(211): Guzzle\Http\Curl\CurlMulti->executeHandles()
#4 /home/mike/src/awstest/vendor/guzzle/guz in /home/mike/src/awstest/vendor/aws/aws-sdk-php/src/Aws/Common/Client/AbstractClient.php on line 286

I’m hitting a bucket in the US East Region.

I’ve tried passing several combinations of curl.options to the factory constructor, but no luck

$s3 = S3Client::factory([
    'key' => '****',
    'secret' => '****',
    'curl.options' => [
        'CURLOPT_SSLVERSION' => 3,
    ]
]);

Server package details: CentOS 6.5 php 5.4.23-29 curl 7.19.7-37 openssl 1.0.1e-16

$ curl --version
curl 7.19.7 (x86_64-redhat-linux-gnu) libcurl/7.19.7 NSS/3.14.0.0 zlib/1.2.3 libidn/1.18 libssh2/1.4.2
Protocols: tftp ftp telnet dict ldap ldaps http file https ftps scp sftp
Features: GSS-Negotiate IDN IPv6 Largefile NTLM SSL libz

Edit: renamed and updated details based on latest findings.