Is it possible to lose continent bonuses after acquiring them?
I know it is possible to have a continent bonus get unobtainable if you lose a country from that continent.
Is it possible to lose your starting continent bonus, or another, if you first acquire it and then lose a country?
You can lose continent bonuses, but not on your starting continent. You can also lose the bonus by allowing the aliens to blow up one of your satellites. As long as you don't lose the game, you will always have your starting continent's bonus.