It sounds like the stepper can't actually do 60 RPM. When you ask it to move a few steps that isn't tested. But when you ask it to move by a large enough increment the limitation appears. Try lower speeds to see if the problem goes away.
I haven't used it, but you might look at the accelstepper library which includes the ability to ramp speed up and down.
How are you powering the stepper motor? What stepper driver board are you using? What voltage is the power supply?
...R