the_title filter returning wrong post type

You have a few issues here

remove_filter( current_filter(), __FUNCTION__ ) is used in wrong context here for what you need to do. remove_filter() unsets the filter from the GLOBALS array once the filter has run once, so your filter is removed after the first run. This happens with spaghetti functions.
You should always return the default filter (or some custom default) value the make sure that something is returned as is should your conditions fail
get_the_title() simply uses get_post to get the post object to return the $post_title property of the object if no post object is passed to get_the_title(). So, instead of using get_the_title() which is affected by the filter, simply use get_post and from there get the post title

I would simply rewrite your filter as follow:

add_filter( 'the_title', function ( $title, $id ) 
{
    // Make sure we are not in admin, if so, return $title
    if (    is_admin() // Check if we are in admin
    )
        return $title;

    //Should work on single product pages, product archive pages, and search pages.
    if ( 
        is_post_type_archive( 'eproduct' ) ||
        is_singular ( 'eproduct' ) ||
        is_search()
    ) {

        $brand_id    = get_post_meta( $id, '_wpcf_belongs_brand-listing_id', $single = true);
        // Make sure we have a $brand_id to avoid bugs and unexpected output
        if ( $brand_id ) {
            $brand_title = get_post( $brand_id )->post_title;
            $title       = $brand_title . ' ' . $title;
        }
        // Either return title as is or our new modified title
        return $title;
    }
    // Make sure we return $title if our conditions should fail
    return $title;
}, 10, 2 );

Just an extra note, you would probably want to wrap everything in a in_the_loop() condition to only target titles in the main query loop

EDIT

I forgot to say, the code above would require at least PHP 5.4 due to direct array de-referencing. The code is also untested

EDIT

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