带有https的YouTube API:“Google_IOException:带有SSL CA的问题

Short form: I've got some PHP code that is uploading videos from my site to YouTube. I'm using the usual Google-provided PHP library, google-api-php-client. I have this code running on two servers; it works on one (https://www.example.com) but has suddenly stopped working on the other (https://dev.example.com), after a period of working nicely.

Details: The code doing the transfer is relatively standard, as far as I can tell: Once the libraries are loaded and some variables get some values, I'm doing:

$client = new Google_Client();
$client->setClientId($youtube_client_id);
$client->setClientSecret($youtube_client_secret);
$redirect = filter_var('https://example.com/upload-to-youtube', FILTER_SANITIZE_URL);
$client->setRedirectUri($redirect);
$youtube = new Google_YoutubeService($client);
$client->authenticate();
header('Location: ' . $redirect);

For the server that's not working, the $client->authenticate line throws the error: Google_IOException: HTTP Error: (0) Problem with the SSL CA cert (path? access rights?) in Google_CurlIO->makeRequest() (line 128 of /var/www/html/example/includes/google-api-php-client/src/io/Google_CurlIO.php).

Other possibly-relevant details:

It seems (to me) that the certificate and access to it should be OK (unless the certificate tester is wrong), so I don't understand where the complaint is coming from. The code and the server configuration has been unchanged for quite a while, hence my search for an external explanation. (I understand that these are Famous Last Words, but whatever.) Any thoughts out there? Thanks!

Potential duplicate question: Amazon MarketplaceWebServiceOrders requests suddenly failing, PHP curl giving SSL CA cert error?

I had to restart the server, not just apache in order to solve the issue.