Platform?
MIDI-CV and CV-MIDI modules doesn’t have stable clocking/timings about their CLK and CLK/N ports (as outputs for MIDI-CV, as inputs for CV-MIDI).
Take a look about this post…
For my new clocking module, it can’t sync correctly from external MIDI source (such my Arturia’s BeatStep Pro, as master clock source). The tempo fluctuates constantly around the real value. Noticed the same behavior by using Impromptu Modular CLOCKED module (set as 24 PPQN, like my BeatStep Pro and MIDI-CV module) as slave.
Concerning Ableton Live, maybe you’ll can consider Link module, or Link v2 module. I don’t have tested them because I don’t use Ableton Live.