Jeff,
it's not that a pellet loses its ability to fly straight at supersonic speeds. It's that it's unable to sustain that speed; the loss of accuracy occurs at the transition from supersonic to subsonic speeds.
In fact, a pellet flying at supersonic speed is plenty accurate. Here's a simple version of what happens when a projectile goes from supersonic to subsonic. When something is traveling at supersonic speed the sound radiating from it "piles up" in a cone behind it- a shockwave. When it happens with a bullet we hear it as a "crack" sound; when an airplane does it we call it a sonic boom. As a pellet drops below supersonic speed the shockwave it built up catches up and overtakes it, buffeting it in the process. In addition there's a range of velocity overlapping the subsonic/supersonic transition; something flying in this range is said to be transonic" as some (but not all) all of the airstream across its surfaces is going supersonic relative to it. Having only some of the airstream across an object's surface going supersonic relative to that object results in unpredictable instabilities. I guess what you should take from this is that
1) a properly stabilized projectile traveling at subsonic speed will do fine
2) a properly stabilized projectile traveling at supersonic speed will do fine
3) a projectile traveling at transonic speed or that transitions from supersonic to subsonic speed will suffer some degradation in accuracy
So to keep a pellet accurate when fired at a supersonic muzzle velocity we need to alter its properties so that it
stays supersonic. And it's not just pellet mass that matters for sustaining supersonic flight. It's the pellet's ballistic coefficient (in which its mass is a factor). The higher the BC, the better a projectile's ability to maintain velocity. Unfortunately, most airgun pellets are deliberately designed to have a
low ballistic coefficient.
Pellets are designed to be stable at subsonic speeds even if they don't have much spin. This is why they have their distinctive diabolo shape- a head narrowing to a waist then a flared out skirt. The flared skirt is a design which deliberately creates a lot of drag on the end of the pellet, helping it to resist changes in its orientation (and therefore trajectory). It operates on the same principle as the shuttlecock you use to play badminton.
Unfortunately, just as in the case of the shuttlecock, this relatively high amount of drag slows pellets down much faster than the bullets that powderburners use. And therein lies the problem. You can shoot a pellet at supersonic velocity, but its abysmal ballistic coefficient means it will slow down to transonic speeds very quickly and experience the negative effects I described above. To give you an idea of just how bad the disparity is, here are some ballistic coefficients (higher BC means projectile will retain velocity better):
7.0 gr .177 RWS Hobby- .011
11.9 gr .22 RWS Hobby- .010
10.5 gr .177 Crosman Premier Heavy- .026
14.3 gr .22 Crosman Premier- .026
100 gr .243 Win spitzer point, Boat tail- .403
165 gr .308 Win spitzer point, Boat Tail- .477
even a 40 gr .22lr hollowpoint (which doesn't have a reputation for being terribly aerodynamic) can have a BC on the sunny side of .140
So the problem really is that you can send a pellet out of the muzzle at an arbitrarily high velocity, but it's going to slow down to subsonic speeds in one hell of a hurry, and as it makes the transition it'll lose some accuracy. Yes, you can hammer out a pellet really fast, but I doubt you'll gain much in the way of accurate range.
Cruising on over to SraightShooters and looking at their numbers for the Eun Jin Sumatra:
.20 cal Beeman Laser (BC .016): muzzle velocity: 1219 fps. @10 yrds: 1033 fps
.20 cal Beeman Crow Magnum (BC .024): muzzle: 1181 fps @10 yds: 1057 fps
the Laser, with its more or less average BC, in only 10 yds, hemorrhaged nearly 200 fps and became subsonic
the Crow Magnum, with its high (for a pellet) BC also, in only 10 yds, already dropped over 100 fps and became subsonic
Okay, so diabolo pellets suck at maintaining velocity. So what about a pellet shaped more like a bullet? Luckily StraightShooters has the BS Cylindrical pellet listed:
.20 BS Cylindrical (BC .023): muzzle: 1132 fps @10 yds 1022 fps.
ouch, the non-diabolo pellet didn't fare so well either. No big surprise when you see its BC, though I must admit I'm surprised its BC is no better than that of the Crow Magnum.
So really, what you need to do to a pellet to give it a better ballisitic coefficient is...
...make it into a bullet. Make it longer, heavier, sleeker. But here again there is a problem. Without that flared skirt, we lose some stability. So how do we make up that stability? We increase it gyroscopically by making it spin faster. But the longer and skinnier the projectile, the higher the spin required. This makes me wonder whether the barrel of a condor (or most any airgun, for that matter) has the proper twist rate to stabilize our hypothetical high-BC pellet.
Now, note that accuracy is relative. Some PCPs have decent accuracy out to 80, 90 yards right? But I'm guessing they're doing that with a big, heavy, fast spinning
subsonic pellet. Heck maybe the pellet
is supersonic at the muzzle. I dunno. But it's still a big, heavy one lol. I don't think there's any way in heck that the pellet is supersonic for very long, however. Just stabilized very well so that it tolerates transonic speeds well.
But to finally get around to answering your question (and some unasked but equally important ones): "
So, my question is with respect to air rifles what weight pellets would be required in order to "fly well" at speeds well over the 1100 fps mark 
??"
Well, they're going to have to be heavy. .22lr heavy. And the gun's barrel will need to have an appropriate rate of twist for that heavy pellet. And they're going to have to be .22lr fast. And the PCP shooting will have to be able to produce that kind of power.
--> And, most importantly, you're going to need a pellet with a stellar ballistic coefficient. I don't know if any of the solid/cylindrical ones fit the bill, but it's certainly worth looking into.
Hope that was coherent enough to help,
Eric
