How is Fight For Your Life time determined?
Fight for your life time reduces each time you use it during a single 'fight'. It appears to reset once there are no aggroed enemies near you, or when you respawn at a New U.
Bleed-out time can be increased with artifacts, shield mods and some team-level bonuses. The number of players in the team won't affect it, but the number equipping Veritas gun or Aequitas shield will.
Player level and relative co-op level have no effect.