What I've noticed over the years is that 300-350 is about as far as any prairie dog shooters hit more than they miss in typical conditions. I've known some that claim to, but I've also never seen them do it when we actually started counting hits versus misses. (I suspect most people unconsciously give hits twice the points as misses, and forget a lot of misses, especially when they hit the follow-up shot.)
If there's no or very little wind it's sure possible to do better than 50% (often much better) at longer ranges. I once went something like 9 out of 12 on some PD's between 550 and 600 on one of those rare afternoons where there wasn't almost no wind. But in a typical high-plains "breeze" it doesn't work that way, and I've shot with all sorts of very fine rifle shots, including national high-power champions, world-record-setting benchrest shooters, and top military snipers.
Part of this is sheer accuracy. PD's and gophers are small targets, and even a rifle that consistently groups 5 shots into 1/2" at 100 yards isn't going to do better than about 2" at 350. (Note the "consistently." That means every group no larger than 1/2,") Two inches is about the width of a good-sized prairie dog, and wider than an average gopher.
That's why I mostly use rifles that do their best work at realistic ranges. I usually start off with a .17 rimfire, either a Mach 2 on gophers or an HMR on PD's, just to keep the nose level down, but when everything in range is either hit or in their holes, usually switch to a .17 centerfire. The .17 Hornet is great on gophers, but the .17 Fireball is better on PD's. Either shoots flat enough that you can hold right on close to the limit of typical "hittable" ranges, whether around 200 with gophers or 300 with PD's. (And yeah, you can definitely watch the bullet through the scope.)
The smaller .224 centerfires also work well with 40-grain plastic-tips at 3000-3500 fps. I often use them as well, whether the .22 Hornet, .221 Fireball or .222 Remington. But none shoot at flat as the .17's, so either a ballistic reticle or dialing is necessary beyond about 200, no matter which .224 you use. But with the .17 Fireball you can hold dead on out to about 275, and on the top edge at 300, which makes hitting so much easier, because as I mentioned earlier, it's often hard to get a really accurate laser reading on a tiny rodent on flat ground.
When most shots typically come at 250+ the .204 comes out. I've found it more effective than the .223, for exactly the same reason: It shoots enough flatter beyond 250 that you don't have to know the range as exactly.
While I've killed some PD's at 500-600 with the .204, it's really at its best out to around 400-450. Beyond that I bring out whatever really long-range rifle I decided on for that trip, and I don't mean a .223 with 68-75's, or even a .22-250, .220 Swiftm .223 WSSM or whatever. Instead it's something that will really do the job, at minimum a .243 and often something bigger.
For a few years I often used a 6.5-06 with 140-grain Berger VLD's at 2950, partly because I was experimenting with it as my longer-range big game rifle. I doubt the VLD's expanded much if at all, but the PD's died anyway. It took quite a few out to around 750, but my favorite hit was somewhat shorter.
I was shooting with several other guys, all of us using "normal" PD rifles from .17 Fireball to .22-250, and per usual after a couple of hours most PD's within 400 yards were underground. But there were some up beyond 400, so I got out the 6.5-06, ranged a big mound with a dog on top that none of the other guys had even bothered to shoot at, clicked the elevation knob and held for what I guessed was a 7-8 mph wind. The other guys knew from the louder bang I was using a much bigger rifle, and most saw the dog flip into the air.
Unless there's absolutely no wind, there's no sense dicking around with little rifles at those sorts of ranges, because a bullet with a BC of over .600 makes things far easier.
