My action had couple of simple (strings and integers) input parameters and had to return one string and one EntityCollection in result. To make action available through WebApi I had to remove all outputs except EntityCollection.
Let’s separate all types of arguments into two groups – simple (boolean, datetime, decimal, float, integer, money, picklist, string) and complex (EntityReference, Entity, EntityCollection). You can have any combination of simple output parameters or single complex output parameter to make your action available for WebApi. In other words if you combine complex output parameter with any other one (including another complex output parameter) your action becomes unavailable for WebApi calls.
To check availability of your action you can use metadata url:
On-Premise with IFD configured – https://yourorgname.yourdomain.com/api/data/v8.1/$metadata
On-Premise without IFD configured – http://yourcrmserver/yourorgname/api/data/v8.1/$metadata
Just open metadata url in browser, wait till page is loaded and hit Ctrl-F to find action you want to check: