I think the possibilities in order of likelihood are:
1. Miswired motor (makes the effective voltage lower). If the motor is supposed to be run in delta and you have it running in wye, then it will see sqrt(3) less voltage on the windings and it will develope a factor of 3 less torque, which may allow it to stall at a lower speed and possibly not trip on overloads. (Obvious way to investigate that: was the motor worked on since the last time you checked speed?)
2. Does the motor have a vfd that you weren't aware of (as Dave suggested)
3. Did you make a mistake on your rpm measurement somehow (try using a different means to check speed).
4. Severely unbalanced voltage or severe high-resistance in series. (Check current balance among the three phases).
5. Extremely Unlikely - Very low applied voltage (but still balanced). Could potentially cause these symptoms without trip but it's a very unlikely scenario to occur. I only mentioned it in attempt to be complete.
All the other possibilities (high mechanical load, rotor bar degradation etc) are a longshot, because at ~1,000rpm, with proper voltage and connections, the motor would be drawing current far above nameplate and should trip on overload within a short period of time. So any of these other possibilities would have to be combined with a severely compromised motor electrical protection system. If you checked current balance in step 3, that would also tell you the current magnitude, which would shed some light on the question of the motor not tripping (if current is indeed far above nameplate then shut down the motor to protect it from damage and check out the overload and investigate those other possibilities of high mechanical load, rotor bar degradation etc).