We did not customize Great Demon Baphomet in terms of the script or its skills. It matches RMS description here. My guess is that one of *three* ways for Great Demon Baphomet to re-enter invincibility triggered, and each of the three modes have their own cooldown of 1 minute.
Our Great Demon Baphomet also got all 3 ways to trigger entering invincibility, again each of them has their own cooldown.
I didn't watch the replay, but going to guess that while the attack mode invincibility is on cooldown, great demon bapho shifted to chase mode for whatever reason and that was sufficient to trigger invincibility again.
And before we get there (and again, I didn't watch the replay so I don't know if this happened for Menace's party or not): yes, great bapho can pull off a total dick move with pulse strike to push everyone away, and definitively enter chase mode to trigger an invincible mode for sure.
It's kind of why we buffed its drops from the default: there's lot of garbage that you need to deal with to handle great bapho. Currently, we have no plans to alter the AI from default, but perhaps we can visit that later.
EDIT: Also, remember that great baphomet is going to use invincibility every 60 second ON ITS OWN, and its cooldown is NOT dependent on when invincibility goes down. The shrine forces bapho's invincibility to go down, but great bapho itself counts the cooldown of when to try setting invincibility back up again. Again, this is how default hercules emulator has great baphomet coded, regardless if that is 100% like official, or like rA (another emulator that other servers may use) handles this issue.