On one of those old Rio / Mark Nelson / strange craft show videos that they did (I'm guessing) quite a few years ago, Mark uses some paste solder and mentions that it can be reconstituted with mineral oil. I have never done that, but I thought I'd pass along the info.
I've used some paste solder, though not often, but I have been using it lately to solder 20 gauge sterling jump rings to make a chain. One thing not mentioned in the original post was the flaming that happens when the binder burns off. Did that not happen or did the poster just forget to mention it?
If it didn't flame off the binder, I would guess that it is indeed too old. (But that's a guess -- I am in no way an expert.)
Edited to add:
Here's a link to the video mentioned above. At about the 2:05 mark, the host asks if the paste solder ever dries out, and Mark answers that it can but that it can be rehydrated with a little mineral oil.
Rio / Mark Nelson video that covers using paste solder