I have a Singer 401A. Great machine.I had this issue a few months back. I found two issues. First, the thread was snagging on the bottom of the spool. There was a small nick which was catching. I flipped the spool upside-down and it worked. Second, there is something with that bobbin. I tried reloading the bobbin, same problem. I tried a new bobbin and voila! Fixed. I don't use that bobbin any more.
I think every machine has a different personality. I hope you find what makes your machine sing!