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From this answer, it appears that the P-51 Mustang takes a lot of altitude to recover from a spin. The average is a 3000 to 6000 foot loss, with a loss of up to 7500 feet in one instance.
The recovery also seems lengthy. From the document quoted in the answer:
The average spin [...] requiring 3-1/2 turns for recovery.
What makes the P-51 Mustang so difficult to recover from a spin?
Others can probably give you more precise info since I'm not a P-51 pilot, but I am studying aircraft dynamics in school right now, so maybe this will help.
Many fighter aircraft are designed such that they are very agile. This is especially true with roll dynamics, where modern fighters are even designed to be inherently unstable. They can then roll faster since the dynamics promote the roll. For roll stability, the wing design is often the main concern. Now, to spins.
I believe spins are mainly a yaw-plane event (though I'm sure there is some coupling of the equations). this means its a rapid rotation about the z-axis, the axis normally considered down. For stability, or desirable spin recoverability characteristics, the tail design is key. I don't know all the details or considerations behind the P-51's tail design, but any number of things could cause slow spin recovery, meaning you need to fall for a while (sorry, pilot!)
For example consider the distance between the tail's centroid and the overall plane's center of gravity. Imagine we added a lot more fuselage, basically extending the tail farther out. Now, with our extended tail, we have a different system. a really long tail might be too resistant to any yaw - basically it wants to got a certain direction, like an arrow.
Now, shorten the body instead, making like a short little squished P-51 with the tail right behind the pilot(shorten the arrow). while flying, the tail now might not help the plane fly very straight, at least not easily.
Finally, put the tail in front of the pilot and try to find anyone brave enough to fly it! No one will want to, because they won't make it home. its like shooting an arrow backwards, or throwing a paper airplane backwards- the dynamics of the vehicle just aren't favorable - any sort of deviation and the instability induces more deviation.
Thats only one part of tail design. You also need to consider size, number of tails, control surface size, and this doesn't even include the yaw dynamics that come from the rest of the plane in a spin.
I apologize if you already understood all that, but maybe it would help with my key idea. That is, that the reason it takes so long to recover from a spin is due mainly to its tail design. I don't know specifically how they designed it, or what design goals they were looking for, but because of what they chose, maybe considering manufacturing ease, structural considerations, aesthetics, drag, turn performance, weight, heck, maybe they just sketched it up and tried it, they ended up with a plane with this yaw plane recovery performance. It might be bad, but maybe their other design goals were met and they chose to live with it.
Other aircraft with better spin recovery performance will likely have different tail features like larger control surfaces, different tail volume... Overall, their tail design will give it better yaw stability and authority (control power available) to recover sooner.
Its late, and I'm sure I've missed things. I hope others can chime in and fix anything I may have mistaken. Let me know what I can add to improve my answer
3 1/2 turns seems pretty good, but factors to consider are:
The P51 Mustang has a similar wing area compared to a Cessna 172, but weighs 6x more.
The Mustang was designed for as low a drag as possible. Great for long range fuel economy and terrific for chasing someone in a dive unless ... the ground happens to get in the way. It also has a somewhat finicky laminar flow wing that could easily re-stall if recovery was not done right.
Then add our natural human tendency to skew distance and height perception (from when a 30 foot fall from a tree was "bad"). 9000 feet is waaaaay up, but 2 miles on a track is no time flat at 200 mph.
Massive and drag slick airliners have similar issues "pulling out" of dives, with rapidly increasing speed even with power at idle. Not much time to recover.
So take a 172 spin and recovery of 1500 feet, and multiply in these factors, and 6000 to 9000 feet is very believable, for those lucky enough to tell the tale.
Comments on tail design are relevant here. Much of the documentation quoted seems to refer to A,B and C model 'stangs for which the tail was basic. From D model and onward, a dorsal fin was added between vertical fin and fuselage to aid in stability and control. Also this is a combat aircraft of some significant mass and wing loading and this may contribute to greater altitude loss than a recreational GA aircraft in a given recovery procedure.
The POH for the P-51 (p. 24) indicates that stalls and spins are easily handled. However, the war stories I have read and videos I have seen indicate that a spin in a P-51 could be quite violent. This often happened during dogfights where the pilot was pulling hard Gs in a turn at full throttle. (See, e.g., this article which notes that "normally understated" test pilots referred to the stall as "viscious".
From what I have read, the reason for this behavior was that the P-51 had "thin" laminar flow wings which can stall suddenly and without warning. (See, e.g., Bradley C Hood, "Fighter Formation Fundamentals" (available online) ["Due to the P-51’s laminar flow wing. It exhibits accelerated stall characteristics much like that of a modern jet fighter."]) In contrast, aircraft with "fatter" wings, like the Cessna 172, have fairly docile stall characteristics.
While a stall is merely the entry into a spin, the wing characteristics that got you into the spin can make it equally difficult to exit the spin. (By "thin" and "fat", I am referring to the shape of the wing cross-section, not the actual dimensions.) (See Anatomy of airfoils and their performance, p. 38 for a comparison of the behavior of thin vs. fat wings.)
(Working at Cessna, I was told that the Cessna Cardinal - which was intended to replace the Cessna 172 - had a similar problem. It had laminar flow wings which were not as forgiving as the fatter Cessna 172 wings, leading to some rough landings.)
As to why the particular spins mentioned elsewhere were especially bad, here are some additional possibilities:
