Can you describe your system and what you were doing when this appeared? Presumably some Audio Files were involved. Are they in some way corrupted, have they been moved or changed, is the HD on which they are stored OK?
Just a few shots in the dark, but please give us some more info.
I have seen an 'error -39' message in other audio apps, and it's usually a sign of a corrupted file. It could be a bad audio file, or the logic session itself is corrupted. Does this happen to one logic song, or all of them?
I've seen that before as well, and I also believe it has to do with a corrupted file. There were several threads on the Digi User Conference about it, (one of them featured you, George - Beat Detective was kicking out this error until you trimmed a little off the front of the audio file you were working on) and scanning through them quickly I learned that it's a Mac OS issue rather than a Logic one, and "The -39 error occurs when the OS finds a disk marker (or doesn't) that signifies the end of the file (or wrongfully so)" according to Jonathan Abrams, who is an Apple-certified techinician and should know.
The bad news is that everyone agrees your only hope (unless it's the Beat Detective issue) is to find an earlier backup of the file you're using that doesn't show the error!
I got this recently in a major audio edit project - tons of automation. It was going to kill hours of work. Upon a bit of research I found the problem to be that the project was coming in via an external firewire drive. When I transferred the project over to an internal drive, the error was gone.
I realize this is not the only cause, but since we have no further information, I thought I'd throw it in there.