One of the projects I worked on failed its Kickstarter, but plenty of the backers asked us to try again and even offered to help out with getting the word out.
Relaunching seem like a perfectly reasonable thing to do. Just make sure you don't make the same mistakes and do your best to read up the dos and donts of Kickstarter. I some guy from these forums did some really detailed posts on the subject in our post mortum. Have a read through his posts in other topics as well...
https://forums.tigsource.com/index.php?topic=45606.0In the end we got picked up by a publisher right after the kickstarted failed and they offered to fund the project... but that didn't exactly go to well for us in the end either, but thats a topic for another day.