I can’t explain it. All I can state for certain is nothing has happened here! I don’t have a Photobucket account (I use Flickr which works fine) so annoyingly I can’t test anything. Hopefully others here who use the service may be able to help diagnose the issue, but I’ve changed or updated nothing here so I can’t explain it just stopping working, nor that older links work and new ones don't.
Can you maybe copy the full links into a post so we can all see them, i.e. don’t use the IMG tags or anything and post the code of an old one that works, and a new one that doesn’t? I’m curious to see if there is anything different about the link structure between the two.
PS Just had a quick look at ‘pistonheads’ and I don’t recognise the software. It’s certainly not XenForo 1.5.x (which is what we run here) anyway.