So I don't actually know what I lose when a country leaves the x-com project. I know I need a certain number of countries in x-com to survive and I know it prevents you from getting the continent bonus but what else do you lose?
If you lose a country due to panic the following things are not possible anymore:
So what you lose is the rewards for those activities and the (theoretical) income if you had a satelite there or where planning to launch one.
You can't rescue all countries, so I say go for those that are most important to you in terms of bonuses and income.