First of all, note that the API only offers 7 days of history. If you’re seeing results on the web that are older than 7 days, they will not be available in the public search API.
Also worth noting that the percentage of Tweets that are geotagged is very small compared to the overall Tweet volume, so generally I’m not surprised that your result set might be small here.
Are there specific examples of Tweets that you expect to find in the API query result, but do not appear?