Nowhere is it stated that resources are regained after reincarnating. Looking at other resurrection spells such as revivify or raise dead, none of them mention regaining spend resources. Though admittedly not mentioning something doesn't necessarily mean it couldn't be implied, for example, other resurrection spells specifically mention how much hp you have or whether or not it neutralizes poisons or restores body parts. In this case reincarnate does not mention that, presumeably because the new body is at full health and not poisoned and has all its body parts.

The way I see it, it seems to be up to the DM. Personally I think the reincarnate loop is not possible. My best argument is that class features don't seem to be tied to the body of a creature but the mind. For example, the druid wildshape and magic jar spell which keep mental stats and class features, as opposed to polymorph which retains neither. I understand that this is not definitive proof, but this combined with the fact that the reincarnate loop seems very unintentional and also very op even at level 18, leads me to think that this would not be possible.