The spell ends when the new form drops to 0hp
True Polymorph says:
Choose one creature or nonmagical object that you can see within range.
This specifies the targeting of the spell; the original creature is a target of the spell.
You transform the creature into a different creature, the creature into a nonmagical object, or the object into a creature (the object must be neither worn nor carried by another creature).
This describes the effect of the spell; both the original creature and the new creature it became are now under the effect of the spell (the sustained transformation).
The spell lasts for the duration, or until the target drops to 0 hit points or dies. If you concentrate on this spell for the full duration, the spell lasts until it is dispelled.
This spell has no effect on a shapechanger or a creature with 0 hit points. An unwilling creature can make a Wisdom saving throw, and if it succeeds, it isn’t affected by this spell.
This describes all the various ending conditions of the spell (expired duration, invalid subject of the spell effect, unwilling target that successfully saves).
Regardless of whether concentrating throughout the entire duration replaces the "or until the target drops to 0 hit points or dies" part of the duration, there is a more general end condition; "This spell has no effect on a shapechanger or a creature with 0 hit points." That is, as soon as any creature affected by the spell has 0hp, the spell ends, and the new creature transforms back to the old.
This end condition could be mistaken for a targeting condition, saying simply that you cannot cast the spell on a creature currently at 0hp. However, this is not a targeting condition; it is an end condition. If it was a targeting condition, it would be placed with the other targeting information (choose one creature or nonmagical object that you can see within range) before the spell effect was described. Instead, it is placed after the spell duration information. It is placed in its own paragraph, showing that it is an over-riding end condition independent of the duration of the spell. Yes, if you attempt to cast the spell on a creature with 0hp, it simply fails at the outset. But if you successfully cast it and create a new creature, the spell ends at any point when the new creature reaches 0hp.
If the new creature takes damage, the spell would normally end before the new creature dies, because the spell ends when the new creature reaches 0hp, regardless of whether the caster managed to concentrate for the initial hour or not.
Note: While this interpretation can be justified entirely based on examining the spell text RAW, it is also supported by a JC tweet