There are many factors in why you can get pushed out of power. I, personally, never get kicked out of office anymore - but the 100% popularity does have a bonus: everyone likes you. That is, all the characters in the game like you (barring hostile foreign leaders and diametrically opposed political party leaders and the like).
This makes getting bills passed in parliament a doddle, for one, and has a whole host of other benefits.
The key to remaining in power, though, is just to do things slowly. Any rapid, excessive policy change is going to **** people off - even if they like you.
The people can like you but still hate your policies.