It just seems to me that air rifles like the Girardoni, which could fire 40 rounds in succession before being de-pressurized, would be such a huge advantage over muzzle-loaders. Wouldn't the ability to fire ten shots to your opponents one be such a huge advantage as to negate complications in training and supply?
I wonder this alot in regards to fast-loading rifles (not just air) in the 19th century.
Well, rifling barrels was pretty hard, and no military factories did it at the time. British Baker rifles from the same period were made by a number of independent gunsmiths. This meant rifles were much harder to mass produce than smoothbore muskets.
As to why the * Girardoni air rifles* didn't catch on, it was partially because of logistics, partially because they were rather impractical and partially because the rifles were fragile.
The air reservoirs used by the Girardoni air rifle was made of iron, and was very difficult to cast and produce, which meant that the Austrian army would constantly be at a shortage of them.
The air reservoirs also took a LONG time to fill with compressed air. It took 1500 strokes of a manual hand pump to refill the reservoir with compressed air. So when you say that they would fire 40 rounds before being depressurized, it means that every 40 shots a rifleman would have to take a long time to make ready again.
There are many reasons for this.
You need to remember that with black powder, there's a huge cloud of smoke after firing - after delivering a volley, unlkess you had a steady wind, it was close to impossible to see the enemy - being able to fire again while not being able to see the enemy was not as much of an advantage as you might think.
As for rifling, before the invention of the minie ball in the 1850s, loading a rifled musket demanded more effort and above all more time than a smoothbore one. Producing rifled muskets were also more expensive. Using smoothbore muskets for regular line infantry thus became an issue of cost but most of all firepower. Rifled muskets remained the weapon of light and specialised units, such as Swedish Jägare or British 95th Rifles.
You'll note that cavalry were first to adapt repeating rifles, partially because they were supposed to be on the move much more than infantry - the cloud of smoke would thus not affect them as much. They were also supposed to be moving rather than standing still and reloading, so their use for a repeating rifle was much highter than that of the infantry.
A black powder discharge also leaves a lot of residue in the barrel - after som 10-20 shots you risk blowing the barrel from the bullet being obstructed by residue unless you clean the barrel - this was especially the case with rifled muskets. This further reduces the rate of fire.
The Girardoni was a complex design that required extremely fine craftsmanship. I seriously doubt any kind of serial production of the problematic air supply could be created. The level of industrial technology and metallurgy had simply not caught up with the design yet.