I agree that the torque goes up on the curve as rotor speed increases (after the pull up torque saddle), so my phrasing about "torque being at a maximum" was definitely wrongly worded.
And although it may have to do with the magnetic time constants, I don't believe it is. The curve is not time sensitive, it is speed sensitive... the horizontal axis is speed, that is. More accurately, I think it has MORE to do with the magnetic phase angles than with the time constants. Both must contribute to the curve.
The speed component rather than time leads one to believe that the torque is constant at each point on the curve, regardless of the reason the motor is running at that speed, or for how long the motor has been at that speed.
So, why does the torque first go down with speed, then increase with speed, before plummeting to its zero at full speed?
I think it has to do with the phase angles of the magnetic fields within the rotor and stator. It is easy to see why the torque goes to zero at synchronous speed; the rotor is not being excited because of the synchronicity between the rotor speed/windings and the flux variations in the stator; there is no induction to the rotor without relative motion. No flux means no torque.
Therefore, as the rotor declines in speed (from synchronous) relative to the excitation current, the induction increases. This should be constant, but obviously, by the curves, it is not (at least the resultant torque is not constant). The rotor's magnetic strength MUST be increasing, though, due to the increase in the relative frequency between the rotational speed and the applied frequency/speed of the stator's magnetic field. Likewise, with less CEMF and therefore greater current, the stator's flux must be increasing as well.
If the magnetics are in direct opposition, then there is no torque, as the flux opposition is directly in toward the axle/axis causing no angular force and therefore no rotation. A slight variation in this angle causes a greater torque, all else being constant. This is what I think is happening at the lower speeds below breakdown torque. The angles of the magnetics (where the torque is really coming from) are becoming less and less tangential to the surface of the rotor. In fact, I think that the torque is sometimes pushing AGAINST the rotation of the motor, causing a resultant decrease in the effective torque.
So, to say this shortly, I think that the strength of the magnets of the rotor and the stator are at a maximum at locked rotor, but the angles between the magnets are causing less of that torque to be transmitted to the rotor.
This is similar to a bicycle pedal transmitting more of its energy on the down stroke than on the horizontal stroke. The vector applied by the bicyclist's foot is tangential to the gear on the down stroke, but orthogonal on the horizontal portion of the stroke. I think similar is happening inside the motor during the "saddle" portion of the curve.
Like I said at the beginning of this post, I think that while the time constant of the magnetics are playing a part in the torque to speed curves' shape, I think its shape has more to do with the phase angles between the rotor and stator magnets.
And, yes, I've been wrong before so it wouldn't surprise me if I was wrong again, here.