Search Widget Display


I have built a website for a research project and on it I have installed the Twitter search widget. Members of the group have twitter accounts and when they tweet about the project they use a common hashtag. I have the search widget looking for this hashtag. It works great, the only issue is that the tweets do not display for very long (3 or 4 days) then they disappear. This leaves this widget blank for periods of time if no one is actively tweeting. Is there a way to get the tweets to display for weeks/months?

On another website some colleagues have a profile widget and a Twitter account specific to the project and it displays tweets up to 40-days old. Is that the way I am going to have to go?

Thanks for your help,