This is quite a well known problem in Warlords. It seems to have resulted from an attempt to make the governor smarter, by encouraging it to run specialists if starvation in the city is unavoidable. Now there's some debate as to whether this is a good idea, but particularly in newly captured large cities it can be sound.
Unfortunately the implementation was extremely crude and poorly thought out. They simply made it so the governor regards food as of zero value if the city is starving, and there are insufficient food tiles available to compensate. This unfortunately means that in the event that a city is suffering even a 1 food deficit (even a very temporary one, say due to the presence of enemy units), the governor removes all the workers from tiles which largely give food, and turns them into specialists, since it sees them as giving better production. It doesn't recognise that it's turning a probably temporary deficit with dozens of turns to fix before a population starves into an immediate problem, with population starving in only a couple of turns. The income from the specialists is not worth the destruction of all the city's stored food, and the loss of starvation correcting time.
The bugged nature of this is especially blatant when the governor starts doing things like choosing to use 1 food 2 commerce tiles when 3 food 2 commerce tiles are available and the city is starving. Since it sees food as of no value during starvation, it cannot distinguish between these tiles, even though one has the obvious advantage of slowing the starvation.
For the human player this is merely very annoying. Every time a city dips into starvation for whatever reason, you have to reset all the tiles. If you don't spot it, you lose a population every turn until you fix it. For the AI though this is extremely damaging, since the governor and AI city management are essentially the same. It usually corrects itself after the population has starved a couple of points, as it eventually recognises there are now enough food tiles to support the available pop (or whatever temporary interference is now gone), but it has wasted a couple of population, and immense amounts of food in the process.
I think Firaxis may have been trying to fix something, but they've drastically broken it in the process, and this REALLY ought to have been spotted in testing. It's blatantly obvious there's a problem with the governor in almost every game I play, and I spotted it within about 20 minutes of starting Warlords for the first time.
I was playing a game as Huayna Capac in Multiplayer and in my second city (Tiwanaku) just got to two population and then it said that the citizens were going to starve when it had plenty of 
tiles it refused to work. 
, or 
), so what's going on? 
