No, there aren't any reasons it shouldn't work with PHP 5.6. We do testing with that version and know many users on that release.
My only guess is that either a permissions issue has changed on the filesystem or a PHP configuration has changed which isn't allowing the fetching of stream entries.
What social channels do you have setup? If it's more than one social network, that helps narrow down that a specific network just isn't working. You may also want to re-authenticate with the social network user on the front-end, just in case the permissions for that user were removed somehow.
Those are my best initial suggestions to investigate, but let us know if it still doesn't work and we'll gladly help investigate further.
Thanks,
Alex