javascript - async.each not iterating when using promises

I am trying to run an asynchronous loop async.each over an array of objects.
On each object in the array, I am trying to run two functions sequentially (using promises). The problem is that async.each only runs for the first keyword.

In the following code, getKeywords loads some keywords from a file, then returns an array of keyword objects. Each keyword object is put into searchKeyword that makes a search. The search result is then put into a database using InsertSearchResults.

In my mind, each keyword should be processed in parallel and the search and insert functions are linked.

getKeywords(keys).then(function(keywords) {
    async.each(keywords, function(keywordObject, callback) {
        searchKeyword(keywordObject).then(function(searchResults) {
            return insertSearchResults(searchResults, db, collections);
        }).then(function(result) {
            console.log("here");
            callback();
        })
    })

})