The problem is more with the pistol than with the caliber.
The M9 failed the trials a couple times before it was chosen for political reasons. The Army and Marines never wanted it - it was forced upon them. One of the arguments that was used to justify it, that the female soldiers needed a pistol the fit their hands, was bogus, since more people seem to find the grip frame on the M9 to be much worse for people with small-to-medium hands than the M1911.
The Design of the M9 is not especially good, being pretty complicated with an overabundance of small or complex springs and parts. The slide decocker/safety is a disaster, and the issue magazines were extremely problematic, except for those built by Beretta. Most soldiers I have known disliked the pistol. It was always real work for me to shoot it well. After shooting an M9 a 1911, Glock, SIG, CZ75, XD, and most other pistols seem amazingly easy to shoot for me. I know many others who have the same experience. I have seen more jams with M9s than any other type of modern, quality pistol I have shot (though I have seen others with some of the more expensive 1911s that had malfunctions very constantly).
As far as a larger caliber goes, I am quite happy with the 9mm. As I am sitting here, I have 72 rounds of 9mm on my body, in four magazines. If I were carrying a .40 S&W, then I would probably have 48 rounds on me now. If I was carrying a double-stack .45, 40 rounds, a 1911, 28 or 32 rounds.
This can be a big deal. A lot of soldiers will carry only two or three magazines for their pistols. This means that a double-stack 9mm could provide double the ammunition that a single-stack .45 provides.
I know from experience that when shooters are faced with a threat, even in training, they shoot fast and until the threat is defeated. Even if a target is dropping, shooters often still fire another couple shots as the target falls, when placed under stress. 1911 shooters tend to shoot as many shots at a target as 9mm Glock shooters do when they are under stress, even when told to conserve ammo in the interest of being able to complete a drill with the magazines that have available.
We also know that there is little difference between the terminal performance of the different pistol calibers, for the most part, so I would never expect a .45 to have a vastly different effect on a target than a 9mm. On the other hand, soldiers are shooting FMJ, so there is likely an advantage in the larger projectile. (Even with HP bullets, we can expect a certain percentage to fail to expand.)
9mm, however, penetrates better than .45 ACP in most cases. This is an important consideration when dealing with targets wearing web gear, magazine pouches, rifle slings, heavy uniforms, flack jackets, etc. No reasonable pistol caliber is going to penetrate some of these things, or combinations of them, but the 9mm will likely penetrate better than .45 ACP, if loaded correctly (some 9mm military ammunition has proven to be on the light side).
So all of the tradeoffs need to be considered, but I think the ineffectiveness of the M9 is more related to problems with the design of the pistol, lousy magazines, and underpowered ammo, than with the 9mm cartridge itself. So the military will have to consider what they are willing to trade off in favor of other advantages:
9mm:
High Capacity
Less Expensive Ammo (only a slight difference due to quantities of metals and powder used, but it adds up)
Easier to Shoot
Good Penetration
357 SIG:
Mid-range Capacity
Very Good Penetration
Seems to have an unexplained advantage in terminal ballistics (I have several ideas about this).
Flat Shooting
Snappier Recoil
Very dependable function - feeds very well.
.40 S&W
Mid-range Capacity
Decent penetration
Slight advantage in bullet diameter
Heavier Recoil
.45 ACP
Lowest Capacity
Less penetration against various barriers
Slight advantage in larger diameter bullet
Heavier recoil (I will argue that most inexperienced shooters are more bothered by .40 S&W recoil than .45 ACP)
Requires larger grip frame
So they will have to consider all of this to determine what advantages they feel are most important. I think it would be interesting to see them decide on the 357 SIG, but realistically, I think they would be served better by 9mm.
Whatever they choose, it needs to have no slide-mounted safety. Price and politics will play a part.
Or, Beretta will negotiate a lower price and they will can the whole program.
As far as revolvers, they are not a great option - there are some troops that depend heavily on sidearms; they need modern magazine-fed semi-auto pistols. Revolvers are not as bulletproof as people think, especially in a combat environment. They are as much or more susceptible to sand and dust as a semi-auto and harder to clean and maintain. There are very few jams in a semi-auto that I cannot clear immediately, but almost any malfunction with a revolver takes it out of the fight. Revolvers are more complicated and more delicate in some ways than most semi-autos. (The M9 managed to combine many of the disadvantages of both.) They are often louder due to cylinder gap and make a larger flash pattern. They are slow to reload without a ton of practice, and extra ammo is not protected against dirt and damaged as well as ammo loaded in a semi-auto magazine.
Lest you think I hate revolvers, I carry a Ruger Old Vaquero for bear protection (and shooting the occasional caribou when my rifle jammed).
However, I spent a few long, cold nights under a tarp on a rooftop behind a scope with one or two other guys. Supporting units were far enough away that there was always a chance I might need to hold out or fight my way out and if it came down to my pistol, I'd rather have the M9 and several magazines than a revolver, any day.