I don't think fopen() can do https ... let me just check the docs ... hmm.. [man]fopen[/man] ... list of supported protocols ... https only since PHP4.3.
That's probably your problem. Anything dealing with https needs a load of encryption/decryption code to do the job; that code is obviously a very recent addition to PHP.
As an alternative to a new version of PHP, with the cURL and Open-SSL libraries installed, and PHP configured to use cURL, you can use that instead.