IE9 should be dropped as well. I'm a web developer too and there's more bugs in IE 9 than there are in Firefox. I still hate Firefox though.Drop mozilla if possible, and use chrome, or Internet explorer 9. Mozilla is the worst modern borwser. I work as a webdesigner, and i face more bugs in mozilla than in IE9.
As per my view you should try to update the version of flash player and check whether it is working or not. If the same problem persists then re-install Firefox and update the latest version of flash player. I am sure it will solve your problem.