By plane he's referring to the angle of the driveshaft from level. If you change the angle of a driveshaft by changing the front or rear connections (raise or lower the rear end, different transmission with a lower or higher rear connector), you can often damage center bearings or u-joints quickly.
That doesn't sound like the problem you have. In the old days center bearings used to go out from too much vibration. Make sure your rear end isn't moving around on you (broken u-bolts or missing nuts on the axle mounts or badly worn springs mounts and shackles, etc.) and the transmission mount isn't worn excessively. If you can move the transmission from side to side, even slightly, by pushing on it, you've got a problem. If you can move the rear end in any direction (up, down, side to side, diagonally), you've got a problem.
Rear ends, when power is sent to them, want to twist upward. This movement is accounted for in the design of the drivetrain, including the sizing of the u-joints, the planes of the shafts and the location of the center bearing. But it depends on all the mounting points being firmly fixed, with no movement of the spring mounts or axle mounts allowed. Wear of any mount point can cause the rear end to move in unexpected ways, putting pressure on the center bearing in ways it's not designed to handle.
Also check all the u-joints. You could easily have a u-joint that's worn excessively, causing a vibration that's wearing the center bearing excessively. Any excessive movement (fractions of inches) translates into a constant vibration that puts tremendous loads on the center bearing during acceleration.
I wouldn't expect extra horsepower to cause this problem. It would be much more likely to shear the tips of the u-joints (which could lead to a bad center bearing eventually but would more likely manifest itself in a broken u-joint very quickly, especially if you're prone to jackrabbit starts or frequent burned rubber.
