I can't duplicate that behavior. I tried it on Safari and Chrome and to test I also installed Firefox on my Macbook. It may be an issue specific to Firefox for Windows but I don't believe it is an issue with "lots of bugs" in the forum software. You may wish to double check any Firefox preferences or plug-ins. I'll add, while testing these, I've had drafts and previews in all three browsers, my text in each was cached in the browser so I could preview, close the browser entirely, open it back up and resume where I left off seamlessly. The content remained unique for each of the browsers so the data is cached locally.
For the record, the Invision platform used here is what we've been using over at Casio Music Forums for almost 10 years. While there are preferences and adjustments that are still being tweaked, I've personally never experienced bugs. The situation here at MPN is unique because the entire database was migrated over so there may be some lingering issues with existing content and dialing in site preferences but this platform is lightyears ahead of UBB.