Sometimes corporate mail servers are setup quite strictly with regards to what mail they let through. As you're on a shared hosting server, your IP address is shared with many other websites, which are all also sending mail. This lowers the reputation of the IP address considerably, and in some cases its blocked by corporate mails servers.
We always suggest clients send through their ISP's SMTP server when sending email, this is completely transparent to the user receiving the email, and its much more reliable as your ISP can authenticate mail sending via your internet connection.
Alternately, you can purchase a dedicated IP address, this will give you a dedicated IP to send email from our servers, which is much more reliable.