How does anyone ever die with a Cleric

I’m relatively new to the game and DMing a group who are all also new to the game, so maybe this is something obvious that we just don’t know. Last session the party was beset upon by a group of assassins in the night. In the ensuing fight, at two seperate times a character was brought below 0hp. Both times, the cleric immediately either healed or cast Spare The Dying on them before they had to make a single death saving throw.

I’m not sure how to proceed because I feel like the way things shook down really undermined any feeling of danger, it seems like the only real way for anyone to die would be Disintegration (or something similar that insta-kills), or for the cleric to be the first to go (though he’s usually quite good about staying out of range)

Am I missing something here, or is it just hard to kill a party member when they have a cleric?

EDIT:

To be clear, I don’t want to go out of my way to kill any players, but I feel like combat is beginning to feel very low stakes, even when up against challenging enemies due to what is described above