Sometimes - with very specific Twitter Feed settings - only a few tweets are meant to be published, so it will be good to go back more than one week showing older tweets anyway.
Folks, our former Wishlist portal, where our users shared their requests and suggestions, was transferred to this forum. You’re most welcome to vote, add new ideas, and leave your comments here — we surely will consider them all! 
Original Votes: 2
Hello Daniele,
Thank you for adding your idea!
Unfortunately, this restriction comes from Twitter directly and at the moment we’re not able to do anything on our end, we really sorry!
However, we hope we’ll be able to find another solution or Twitter will loosen the restrictions.
Thanks for your help!
Helga, Community Manager
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Right now it’s only possible to pull posts for the past week when the source is a hashtag. That time period should be longer.