Can the Regenerate spell bring someone back from the dead?

The description of Regenerate states:

You touch a creature and stimulate its natural healing ability. The target regains 4d8 + 15 hit points. For the duration of the spell, the target regains 1 hit point at the start of each of its turns (10 hit points each minute).

The target’s severed body members (fingers, legs, tails, and so on), if any, are restored after 2 minutes. If you have the severed part and hold it to the stump, the spell instantaneously causes the limb to knit to the stump.

So as an example, instead of Death Ward, a Cleric casts Regenerate on a Fighter going into battle where they are hopelessly out matched.

The Fighter puts up a good fight, but brought to 0-hp, then two point-blank attacks mean immediate 4 failed death saves, all within a single round of combat. Therefore the Fighter is “permanently dead”.

But can Regenerate bring them back?

A dead body is considered an “object”, not a “creature”. But the spell was cast while the Fighter was alive and thus a “creature” and can be a valid target of the spell. Beyond the casting, the spell only says “target”. So it should no longer care about whether the Fighter is a creature or a bloody, dismembered corpse.

So every round the Fighter stands back up with 1-hp saying, “I can do this all day.” Or does death invalidate the target as they no longer have a “natural healing ability”?