Sorry for the slow reply. What browser are you using? And which recorder are you using? How long are your recordings? There are many things that can go wrong with recording. Most of them are at the browser end of things.
Did you try rebooting and using a different browser? Google Chrome has a permissions dialog that is very hard to see. It pops up when you first try to use your webcam/mike on a site. It appears just beneath the address bar in the browser. Almost everyone misses it, even I forget about it. And of course there is the standard flash permissions dialog. If permission is not granted to the camera/mic then the recording will usually fail in the way you describe.
Also if Skype or another application is trying to use the webcamera, it can be unavailable for the browser. Sometimes it happens that the other app doesn't release it. Even when the other app is closed down the camera is unavailable. I wonder in these cases if there is a problem with the driver software. I sometimes get this on my mac. Anyway, rebooting and trying a different browser are good steps to take.
Finally depending on the recorder you are using, try not selecting "mp3" or "mp4" on the recorder. Sometimes the conversion process is failing because the server is too busy, or the recording too long, to respond before the browser gives up waiting.