Ever worked hard for a 9-11k Level 1-1 score, only to suffer a textbook rivet screwing on the very next screen? Of course you have. Everybody has. Level 01 scores of 14-15k (9X00/5X00) have become so common that I scarcely take notice anymore. I'll accept it, but I don't have to like it.
A recent game presented a sharp contrast. I put up a 7200 on Level 1-1. If I've ever had a lower 1-1 score, taking both hammers and pressing aggressively, it's been completely erased from my memory. Short of taking a wild barrel in the face, everything went wrong. The bottom hammer was weak, steering was a joke, the initial fireball was determined to make my life miserable from start to finish, and zero-point barrels were all over the place. I played on, managing 13,400 on the rivet stage and completing Level 01 with 20,600 points. Not bad at all. It wasn't the first time the rivets have bailed me out after a disappointing 1-1, but it probably represents my most extreme example.
An early death almost always means an automatic restart. For me, a poor score on any individual stage does not.