I'm using the Point Distance Analysis tool instead, and keep getting an empty output table.
Previous users with the same problem have suggested exporting both feature classes into the same pgdb, or closing the program and re-opening it. I've tried both, with no joy. It's possible that the dataset I'm using is simply too large (2 billion-odd points), but others appear to have managed it successfully.
If anyone has any suggestions, I'd love to hear them!