I assume you are talking about a pistol for a powerful cartridge; obviously there are many fixed barrel auto loaders for .22, .32, and .380 as well as 9x18 Police and 9x18 Makarov. There have been fixed barrel pistols for 9x19 (9mm Luger), including the old Astra 400, 600 and 800, the H&K P7, the Steyr GP, the gone and unlamented Rogak, the High Point, etc. High Point even makes blowback pistols in .40 S&W and .45 ACP.
The Luger has a fixed barrel only in that the barrel is attached to the recoiling receiver; it is still a locked breech, short recoil action, not a blowback.
The "hurdle" is pressure. Like any firearm, the auto [loading] pistol has to be made with a breech that will contain the pressure generated by the gas from burning powder. In, say, a bolt action rifle, the method is obvious. But in an auto pistol the designer wants the breech to open automatically so the empty case can be extracted and ejected and a fresh round inserted in the chamber.
The problem is that if the breech is allowed to open while the pressure is still high (before or even just after the bullet leaves the barrel), the cartridge case can come out far enough to expose its weak sides and it will blow apart, wrecking the gun and possibly injuring the shooter.
So the idea is to prevent that. In what is called a "blowback" action (low power pistols), the inertia of the breechblock (usually a slide, but it can be a bolt like a Ruger .22) is enough to hold the case in until the pressure drops. The case is allowed to just blow itself back out of the chamber (hence the name "blowback"). The extractor is not needed except to remove an unfired round, and blowback pistols have been made without an extractor.
In high power pistols, the usual method is to lock the barrel and breech together by some means until the pressure drops. That type of pistol operates by recoil, not pressure. In a Model 1911, for example, recoil begins as soon as the bullet starts to move, and while the bullet is moving down the barrel, the barrel and slide are recoiling together. As the bullet leaves the barrel, the barrel and slide are unlocked, the slide continues back on its own momentum to extract and eject the empty case and then comes forward under spring pressure to pick up a fresh round and again lock with the barrel.
There have been high power pistols made to operate using gas, but the majority are locked breech, short recoil systems as described above.
So how does High Point get away with a blowback action for high pressure cartridges? Remember that about a blowback pistol depending on the inertia of the slide to keep the pressure contained long enough? Well, inertia depends on mass (weight). Most designers didn't want to make a slide of enough mass to contain high pressure, since that would make the pistol awkward, heavy, and hard to hold. High Point did.
Jim