This API integration operates over port 80/443. These are the standard ports for http and https.It is quite possible that your hosting company are blocking the requests.
After many months of Masher posting to WordPress, seeing different errors such as "Forbidden" and "Unable to Post", it is 99.9% of the time (100% really, but allowing for the exception), a hosting issue.
Also, check the hosting company for Firewall blocks.
WordPress Integration
WordPress Integration (Recommended)