The WordPress app utilizes the xmlrpc.php file on your account put there by WordPress. However, a lot of hosting providers are now forced to block this file for security reasons.
As a workaround you will need to download the plugin named Rename XMLRPC and install it to your account. The easiest way to do this is to access your WordPress admin area (typically at www.yourdomain.com/wp-admin/), then click the "Plugins" menu option in the left hand column. Click "Add New", then search for Rename XMLRPC. Click "Install Now". DO NOT ACTIVATE THE PLUGIN YET.
Now that the plugin is installed but not activated, login to the File Manager section of your control panel (www.yourdomain.com/cpanel) with our services, or login via FTP client, and navigate to your WordPress installation folder. In most cases this is the public_html folder. You may have installed WordPress to a subfolder. If this is the case navigate to that folder.
Find the file xmlrpc.php
Rename it to xmlrpc2.php
Close the WordPress app on your mobile device.
Now go back into the Plugins area and activate the Rename XMLRPC plugin.
Now try using the WordPress app.
You're done! Happy Blogging!
If the steps above do not work, Go to file manager (or in your FTP program) and edit the file wp-content/plugins/rename-xml-rpc/rename-xml-rpc.php
Verify the file name in this line of code...
$renamed_xml_rpc_filename = 'xmlrpc2.php'; //CHANGE THIS pointing to the renamed file
If the filename does not equal xmlrpc2.php change the name to xmlrpc2.php and save the file.
xmlrpc2.php is the default name at the time this article was written.