Set Arp Hold to ON - Arp/Common screen.

I'm not sure which Montage you own (the new M or the classic non-M).  I'll just answer for the classic since that's what I have.

Check your "MIDI Signal Flow" chart.  The Arpeggiator (highlighted in yellow above) needs to be in the path of MIDI In as shown.  You can see that MIDI notes coming in (from the DAW) can make it to the arpeggiator.

One wrong setting would look like this:

... notice how the Arpeggiator cannot be reached by MIDI In.  It's only connected to the keyboard so the DAW, in this case, couldn't trigger the Arpeggiator.

Ignore the rest on the screen - it's only the "MIDI Signal Flow" that's of interest.

This isn't an exhaustive run-through.  But it's probably a top contender of what could be setup incorrectly.

@Jason - Yes - it wasn't clear to me just what configuration was being used so I just mentioned the Arp HOLD in case that was it.

 The Arpeggiator (highlighted in yellow above) needs to be in the path of MIDI In as shown.  

As discussed in a previous thread the M models no longer have 'Arp Midi Out' that would be needed for the use case you mentioned. There was an IdeaScale suggestion submitted to bring that parameter back.