Hello Anastasia,
let me try to help you. (I am in no way affiliated with Session Buddy, just a former user).
1. Have the Session Buddy page in front of you
2. Open the DevTools. You can press F12 or Ctrl-Shift-I or use the menu in your browser.
3. Select the Console tab on top (the first tabs should be "Elements", "Console", "Sources" etc.)
When you have the right tab, you should be able to type stuff at the bottom where the ">" is on the left hand side.
4. Type the thing: saveData() (and press Enter)
5. A file should be downloaded to your download directory. That would be the export of your stuff. It is essentially the same as using the export button in the Session Buddy menu..
I doubt that it will bring any of your lost data back. The safest way to not lose data with Session Buddy (as I doubt the problem will be fully fixed anytime soon) is to export your stuff each and every time you save your sessions.
Let me know if you found the Console thing and if anything worked out for you.
Hope that helps.