We ran into this issue as well, even after placing the IP originating the request into the allowed hosts list. It was not until we came accross the following that we changed our settings:
Administration > Admin Access > Allowed Networks
Use this window to set the networks that can access the MultiModem iSMS. The administrator can then add, edit and delete any network. By default, the LAN network is always allowed access to the MultiModem iSMS. In addition, the administrator can configure the IP Address and Subnet Mask as 0.0.0.0 to allow access to any network.
We subsequently configured the IP Address and Subnet Mask as 0.0.0.0 to allow access to any network and requests started to succeed.