Best approach for pulling in all Tweets with a specific hash tag?



I’m currently developing an application where uses can create hash tags to track, and the site will display them in a pseudo-realtime stream for the user. Something like what live events project onto screens and attendees can post Tweets to using a given hash tag.

Currently I’m using the REST search API, but it often misses Tweets and doesn’t pull this in. These seems to be because the search api doesn’t index everything. Obviously this is a problem for my application and makes it seem as though it isn’t working, even though it’s out of my control.

With that in mind, is there a better way to handle this issue. Ideally any number of people could create track-able hash tags and have this pseudo-realtime feed. My main goal is not not have Tweets be ignored and not show up on the screen.