I'm using Mantis 2.11.1 on a Windows Server with IIS 8.5 and php Version 7.0.21. I have enabled the REST API ($g_webservice_rest_enabled = ON;), created an api-token and tested the API using Postman.
For the call http://srvmantis.polymania.com/mantisbt/api/rest/Issues with the header Authorization:myAPIKey I get '404 - File or directory not found' as result.
I had the same problem and I've solved it this way: first install/enable URL Rewrite in IIS if you don't already have it then put this in the web.config of Mantis in the system.webServer section:
<rewrite>
<rules>
<rule name="redirect to api" stopProcessing="true">
<match url="(.*)" />
<conditions>
<add input="{REQUEST_FILENAME}" matchType="IsFile" negate="true" />
</conditions>
<action type="Rewrite" url="api/rest/index.php/{R:1}" />
</rule>
</rules>
</rewrite>
hope this helps
bye Cristian