Sometimes, when I put a lot of pressure on my pedals while accelerating or skidding, my pedals "drop" like when your cog is unscrewing. I have a lock ring, so it's not unscrewing. I've recently changed my chain. Do you guys know the problem? I can't ride like this. I can send photos if needed.
I can think of six possibilities (however realistic each may or may not be, and not in any particular order) for crank advancement through an angle out of proportion to the driven wheel in a fixed gear setup...
(1) 24TPI hub threading not fully bottomed by the cog as it should be. The reverse-thread lockring, if all parts are truly tight, should prevent this altogether, but tightening the lockring would not necessarily ensure the cog is bottomed against the hub shoulder (since the cog won't cooperate by going ahead and tightening [like axle cones often do] if the lockring is tighened against it while loose). I have not experienced this, but since the lockring has a left-hand thread, I assume it could be loose from the cog without immediate catastrophe. The cog would then be allowed to rotate on its screw threads through a small range, but it could not completely unscrew because of the reversed thread conflict. The scenario provides that the cog is intermittently screwing back and forth between 2 shoulders (and both ends of this range might feel like freewheel threads being tightened [with alternating direction] when torque application is reversed). Hypothetically speaking, a same-threaded locknut would not do this, but rather be free to unscrew by the impetus of the next nut over (which would be the cog), and the results WOULD be catastrophic.
This seems pretty possible to me. If I install a freewheel by hand, even using a chain whip, I can still feel it tightening when I start riding and get my weight and leg muscles into it in the normal drivetrain usage. This suggests that if a fixed cog were applied using only hand strength, and then a lockring were immediately applied, perhaps that final tightening takes place after the lockring is set, and since post-tightening of the cog causes the "nuts" (cog and lockring) to be DIVERGENT, there would be room for what I described since it would be free (enough for leg power at least) to untighten from the hub and tighen against the lockring under back-torque. Assuming you have brakes, my suggestion is to use leg force to tighten the fixed cog and stop with the brakes (or whatever it takes to avoid any backpedaling) and then re-tighten the lockring and ride as normal to see if the problem goes away. Without brakes, find a way (like do it uphill, or use impact if you can fashion some kind of boss or linkage to the cog) to maximize tightening torque before the lockring is finally snugged. Make sure the threads, as well as the faces of the cog and lockring, are clean and there are no spacers or anything but hard surfaces for bearing the torque.
(2) I have not heard of this happening other than in my imagination, but it seems pretty conceivable that perhaps the soft male threads on the hub have worn [stripped] sufficiently to allow the driven cog to skip over them under sufficient torque. This would be more likely if the bike had previously been ridden with the rear cog and lockring inadequately tightened. This would effectively require hub replacement in any hub I have seen (where the male threads are a permanent and fundamental part of the hub body. Even just short of tight, there is often noticeable play in these threads, which is why I imagined this possibility.
(3) Chain skip, which I think was hinted above would require a pretty extreme pitch mismatch in a single speed train in order to ride on the tooth peaks without trough engagement. It's a remote possibility, and you would probably hear an ugly metallic racket as this took place. Moreover if your chainline is imperfect, this could easily result in a thrown chain. edit: If this is possible it would imply that the chain is already WAY too loose.
(4) Tire slippage is possible (however unusual in an inflated tire), and might feel a little like thread friction (also being a quiet phenomenon). I have seen tires [that don't have much "gum" over the carcass material in the bead area] with low inflation be able to slip on the rim under torsion. Not much of this would be possible before damaging the valve stem if the tube goes along for the ride, but if it stays with the rim (less likely), the tire could slip infinitely. Most tires stick pretty well but I have seen exceptions. This is the reason for rim-locks in fat low-pressure tires. A test of increasing inflation should eliminate this possibility.
(5) I have definitely experienced a type of crank wear that could feel like this (but only for your left foot). In conventional square-splines, if you do a lot of standing, jumping, etc., with your right foot forward, the torque in the spindle is reversed from normal pedaling action by any downward force that ends up evenly distributed between both pedals (as in, coasting NOT pedaling). (Keeping your left foot forward as a general rule when standing negates this possibility) The soft square-taper-broached holes in the crank arms can develop play on the spindle and then the left crank is allowed to swing through a dead angle (relative to the right crank's constant chain engagement) that may feel similar. In very minor cases, the spindle cap screws or nuts can be tightened down harder to "cold-form" the crank arms (they're pretty much toast by this point anyway but you can get home on them by doing this). In more advanced cases, I have used a piece of an aluminum beverage can to shim the tapered hole and hard torque to remedy. Ultimately the condition necessitates crank replacement. *edit: I think this problem is more likely with the older "nut-on-stud" crank attachment to the spindle since the serrated side of the nut reacts to any crank movement and provides a quick foothold for development of slop. I changed my habits away from having my right foot forward while standing at about the same time as I started using a cap-screwed (rather than nutted) bottom bracket, and I have not had this problem since, so I'm not sure how likely it is in other cases.
(6) Backlash from chain being too loose. The chain should always be loose enough to not be taut at the tightest point (found by rotating the system until the minimum chain play is found - play adjustment should be made at this rotational position only). If there is eccentric wear or manufacturing fault in either sprocket, this could be more extreme but there still always has to be at least slight play. If the variance is extreme, then at the loosest rotational phase of the system, there would be considerable backlash, the 'dead angle' which the cranks must subtend between application of forward and rearward torque (regardless of rotation position or speed - it's the transition from the slack being at the bottom run of the chain with forward drive to it being at the top run of chain with rearward drive, regardless of actual movement). This would not feel "frictional" like the hub thread tightening phenomenon, but more like a free angle between abrupt endpoints, like when you switch from coasting to pedaling on very coarsely pawled freewheels or freehubs.