Hi I have same setup but windows instead. I have found that tempo stability is much better if you use the beat step as the master tempo for Ableton and anything else in the midi rig. The additional benefit is transport control over session clips too.
Also, on page 51 of the bsp manual it says:
When the external source is not running, BeatStep Pro will function according to its own internal clock at the last known tempo.
Finally in slave mode the bsp is listening for all tempo instructions from any source, so look at your other hardwares and if they are sending tempo.