"The reduction lasts until the target finishes a Long Rest."Just from a rules lawyering perspective, "The target dies if this effect reduces its hit point maximum to 0" is a trigger, not a status effect. At the moment the vampire reduces the hp maximum to zero, the target dies. If the target is later raised, then even it it remains at 0 hp, the "die when you are reduced to zero" no longer applies because the triggering condition was not met. There is no general rule that you instantly die whenever your hp maximum is zero.
The triggering condition is still present until a long rest is completed, which the corpse cannot do because, well, it is a corpse. If you raised the target, which is still at maximum 0 hit points due to the vampire bite, it would simply die again immediately since that is the effect of the vampire bite.
The effect of the triggering condition is why our DM is ruling Greater Restoration is required (to restore the loss of hit points from the vampire bite) and it will have to be done just at the completion of the Raise Dead so both spells are completed simultaneously.
Otherwise, in general, at 0 maximum hit points, you would be unconscious until your maximum hit points were raised above zero.