Just a thought,
Are you doing missions for a reason and please try not to use acronyms?? Missions can be very specific and if you do the wrong type for a war, election, coup etc then they are of no value and if other factions are doing the correct missions then yes, influence will go down.
Thinking as I type, when is an adversarial state, should our influence be locked? I for one have been in a war and without doing anything our influence increased by 5% although I am assuming Faction Reputation?? stayed static because each day showed as 'DRAW'.
The 5% increase in influence counting for absolutely zilch. (This was influence gained DURING a war and not awarded at the end)