Which search provider are you using?

(The standard recommendation of course applies: upgrade )

Is your index filling up when you go to  /episerver/cms/admin/indexcontent.aspx.  I would check to make sure you are not using and old version of the index and try to re-index all the content.  This might help.

@Erik I'm using EPiServer Find as my search provider. EPiServer Search is not active - does it need to be in order for the media search to work?

@Joshua I don't think the index is filling up. When I navigate to /indexcontent.aspx, the last complete index date is blank. When I click on "Start Indexing", nothing seems to happen but I also get no errors in EPiServerErrors.Log. I definitely don't see an index getting built up on disk (I thought it was supposed to be under App_Data but it isn't in my case), but perhaps with EPi Find I wouldn't see this anyway. 

This is often a source for confusion but the way i normally explain this is that Episerver uses three search providers:

1. Search provider to be used on the site that the users are supposed to query, populated by the scheduled jobs in cms admin.
2. Search provider to be used by the CMS backoffice containing pages, blocks and assets, populated by a hidden one-time indexer and kept updated with events.
3. Search provider for commerce backend, contains products, packages and variants.

I have no personal experience of Find but I assume you mean that you use Find for 1. It should be possible to use it for 2 as well but might require further configuration.

It is possible to install and activate Episerver.Search for 2 even if you have Find for 1.

(I have successfully replaced 3 with an extended version of 2 that also included nodes, i.e. categories and brands.)

Thanks for the responses. I've found that it is Find that is controlling the media file search. The problem was that someone had switched off the searching of media in config under:

Under Business -> Initialization -> FindInitialization.cs I have the following code block:

    [InitializableModule]
    [ModuleDependency(typeof(EPiServer.Web.InitializationModule))]
    public class FindInitialization : IInitializableModule
    {
        public void Initialize(InitializationEngine context)
        {
            //Bugfix: these have been commented out so that our media gets indexed (needed for the CMS media search)
            //ContentIndexer.Instance.Conventions.ForInstancesOf<ImageFile>().ShouldIndex(_ => false);
            //ContentIndexer.Instance.Conventions.ForInstancesOf<MediaData>().ShouldIndex(_ => false);
            
        }

        public void Uninitialize(InitializationEngine context)
        {
        }
    }

So basically the company we inherited from were deliberately not indexing media files - possibly for performance reasons or to avoid a large index.

If you check the Find index, are files indexed? In Admin mode/Config/Search Configuration. What providers do you have enabled?
Is find for files enabled? Try disable the standard search and just have find providers.