In the core rules for Call of Cthulhu, the entry for ghosts (p205) is one where the Keeper is encouraged to tailor-make the entity to suit the circumstances and the flavour of the campaign. The basic entry describes ghosts as having two traits (INT, POW). This provides a lot of latitude, and allows each ghost to have different classifications, abilties, and limitations, organized within a lose framework of ideas.
In the base example provided, the entity attacks to drain POW from victims by using the Resistance Table. If the attack succeeds it may be allowed to gain POW (the characteristic) and if it loses, its POW trait is decreased. This sort of construct is quite useful for the idea of a vengeful spirit, such as the Wraith that they mention in the rules on page 211. Alternately, this attack may just reduce the traits of the victim and provide no benefit to the entity. As a result, some ghostly entities may grow more powerful over time, while others will slowly fade away.
If the Keeper decides that the entity should be able to produce effects beyond the draining of POW or other characteristics, Magic Points may be provided for that purpose. When these have been completely expended in the game the entity loses coheshion and vanishes for a period of time. A week is suggested in the entry on Wraiths. Magic Points regenerate, and as they are replenished, the entity regains the ability to manifest according to its nature as determined by the Keeper. The Keeper may determine at what rate these points regenerate, or may simply have them regenerate at the same rate as they do for Investigators to keep things simple.
Lost POW does not regenerate. Once a ghost or similar entity has lost all of its POW it is destroyed. Similarly, the Keeper may rule that an entity has been dispelled permanently if all of its Magic Points have been depleted. As always with this type of creature, it will be on a case by case basis as suits the needs of the Keeper for the ghost in the overall fabric of the tale.
In my own games, I like to make a distinction between sentient and non-sentient ghosts and have them interact with the world differently. A ghost they merely recreates an important scene from its living days has characteristics tied to others' memories of it, and so will eventually cease to exist once the details of its life have been forgotten by the living. One that was created by violence, and concsiously seeks revenge, may be quite able to grow into a genuine threat with a signigicant POW score harvested from those it preys upon, and may be tasked with choosing to rest once its quest is done, or to continue to roam in an endless cycle of revenge and rage. The options are quite open. The entities may be tied to a location, or tied to a person or object, or "free-roaming, full torso apparitions" haunting much wider areas, or limited areas which are not immediately obvious to the living.
Based on CoC itself, I would say that:
- POW does not regenerate when lost and is the baseline of durability for the ghost - once it is gone (by whatever means) the entity is gone.
- Magic Points do regenerate over time (as set by the Keeper)
- Magic Points may determine the temporary or permanent dissolution of the entity, as appropriate
Based on CoC itself, I would say that the base assumption is that Magic Points regenerate as they do for Investigators but similarly to the characteristic of POW for Investigators, once POW is lost is does not regenerate, it must be regained by other means. No special rules for MP regeneration are provided, and much leeway is given in creature design, so defaulting to the base rules for Investigators, or inventing special circumstances is expected. As Kyle Willey states in his comment on the question, the most common way for a ghost to increase or replace POW would be to steal it from the living, or receive it as a sacrifice.