This question has been asked millions of times and the answer remains no. Some people have said there are apps that will allow you to retrieve or find old Snapchat stories you shared weeks and months ago but these apps do not exist. Once your story disappears I have yet to find a way to bring it back. This is unfortunate, but that is the whole point of the app.
If you find any apps that actually retrieve or bring back your old Snapchat Stories please comment below with the name of the app; I would love to try it out. At this point, you will have to either save your Snapchat story to your smartphone or download it to your computer. If you want to relive those old Snapchat Stories you are going to have to do that with your memory.