Megacorps you own can decrease reputation when advertising for enemies.

[Anna Bakker]

When taking over a megacorp (The Construct for example), their reputation is set to 100 and you are no longer able to advertise for them. But advertising for their enemies still decreases your reputation with them, and you can't advertise to get it back.

[Riot]

This is not a bug. You can still lose favour with a corporation you bought out by acting against them - you need to plan carefully to avoid shooting yourself in the foot by advertising for your own competitors.