It's not so much that there's nothing to shoot at, but rather e.g. a boss or one of his subsystems that you can't destroy in time anymore, even though you are technically surviving up to that point. The lifebar analogy doesn't work, since a lifebar wouldn't continuously decrease. I don't know, of course it doesn't happen often, but it's just really weird. Would have preferred the game without the time mechanic and they could still have used all the time based powers.
Ahhh, I think I've encountered the exact problem you're talking about.
I kept dying and continuing on the big... crane like?... boss about 3 stages in... and based on the checkpoint I'd hit, it didn't seem like I had enough time or targets... but after trying some different strategies, I found one that let me scrape by and make it out after beating it, even after taking a few hits.
The life bar analogy is fine. It's a fact: the clock is your health and as such:
There are no health pickups, there are time pick ups.
When you take damage, it takes time off the clock.
The clock is your ship's life. Period. When it runs out, you die and must continue.
I believe the Shinobi game on PS2 was like that -- your lifebar was always decreasing and if you didn't kill/move with enough speed and skill, you died because you took too long. Fact is
To me, the time mechanic is what really sets it apart from everything else and large reason of why I like it.