I admin several dedicated servers and run an SEO business, the issue is a little perplexing, but it shouldn't be too hard to fix. Switching hosts/re-indexing the pages is definitely NOT the issue. Either the forum software or the web server (Apache or NGINX) is. That's what's throwing/returning the 404. Simple Machines Forum (SMF) software is several versions from current/stable, I'd update that first and see if it fixed the issue. I believe there's an active exploit in the version of the software TFF is using, so even if updating didn't fix it, it wouldn't be wasted time. Clues to the problem surely lie in the error logs.
I'd be happy to help, someone can send me a PM to discuss. Google is definitely penalizing TFF in the SERPs now. Since the last big update came through in December, TFF topics have disappeared. This site also needs to get an SSL cert asap and start serving content securely. They are free these days and easy to implement.