What do I lose for losing a country?
If you lose a country due to a level 5 panic rating during council reports, the following things are no longer possible:
- Launch a satellite there to generate additional monthly income
- Complete any missions in that country
- Receive requests from that country to fulfill
- Secure that continent's bonus
So what you lose is the rewards for those activities and the (theoretical) income if you had a satellite there or were planning to launch one.
Sidenote:
You can't rescue all countries, so I say go for those that are most important to you in terms of bonuses and income.