Why am I not seeing more keywords returned in Popular Searches?

You may need to increase the threshold settings for Popular Searches.

To do so, go into Workbench > Keyword Search > Autocomplete and click on the Update Popular Searches button:

From here, you can specify the date range that Hawk should grab from, along with the minimum number of times a keyword must be searched in order to be returned in Popular Searches:

Be sure to rebuild the index for your changes to apply.