When empires are at peace then it is reasonable that colonies should enjoy some degree of freedom when deciding their allegiance. One can imagine votes for independence and all that sort of thing. 

During war, however, attitudes harden. Patriotic fervour takes hold and the people rally behind the troops. Secessionist movements are seen as treasonous. Seditionists are rounded up and shot.

Therefore I suggest a change to peaceful conversion during war: a penalty is imposed when inside the enemy's influence rather than a countdown to colony loss. 

For example, a constant manpower reduction, similar to what happens when under siege by ships, to represent the cost of suppressing dissent. Then, if the influential empire wants the colony, they would have to send an invasion force to consolidate their hold. An easy invasion if all the manpower was used up dealing with the rebels, but nevertheless it would still require an action.  

Sitting pretty and acquiring the whole galaxy without firing a shot is a bit cheap, especially if there are few effective counters. Invading the influential empire and taking their systems doesn't reduce their offensive influence fast enough to defend against colony loss.

In short, what I am suggesting is that war should put some sort of pause on peaceful conversion.

I would move this forward a little and change the way conversion is done right now.

Currently you have percentages running and once they reach 100% the system changes owner.

That is far from I would call reality.

During peace (cold war not included) conversion should be happening like this:

1. Colony approval decreases incrementally as they want to become part of the other empire
2. When colony approval goes into "rebelion" then the conversion process starts

I would see the original owner of the system having a choice of either putting military in place to kill rebellion (reduce foreign influence but also lose population) or trough diplomacy offer the system to the other empire for dust/technology/other system or anything else.

If no action is taken I wouldn't automatically make the system part of the other empire. They could rebel into becoming a new minor faction that is supporting the empire they like (FIDS generated for them?)

The reason why I would not see the system become property of the other empire right away is initiating a wave of influence take over. 

There should be a way to fully assimilate such a system but it shouldn't be right away.

Of course at cold war such a take over would be still possible but the approval decrease would be a lot slower.

And in war there would be no such decrease.
This doesn't chance the fact that a system under influence zone of another empire if in rebellion wouldn't decide to leave your empire.

Maybe even it is worth considering that any start system under "rebellion" approval can leave your empire.