With income of -35 gold a turn, I'd say that yes, you are likely in an unwinnable situation. This game did not promise that you could win from any situation, no matter how impossible-seeming.
I've beaten Chapter 3 on Normal, and tried a few Custom Campaigns on it as well. My strategy suggestion is as follows:
1) Move the Armours/Transports on the island to the capital.
2) Move your units SW of the island to the capital.
3) There are 3 territories that are occupied by only Troopers. You can't defend them, consider those countries lost for the moment. Send those Troopers to reinforce the nearby countries that have stronger units.
4) Your forces should now be concentrated in 3 countries, all of which have War Factories (or are your Capital. Build units there to bolster the weaknesses in the rock-paper-scissors matchups. (If a country has Hunters, but no Armours, build Armours.)
5) Hang on and hope for the best.
