Note that the coloured block in the corner of the counter. If it is BLACK it should be a warning sign for you.
It triggers for any substantial lack of supply. Even if the food is getting through, if you are short in the SHQ on munition, fuel or energy it'll colour the block black because it can't deliver any.
There's a difference between 'this unit is not fit for combat due to lack of supplies', which is inconvenient and means you need to be careful about your battles, and 'this unit is dying due to lack of food', which means you have to expend any combination of recruits, metals, rare metals, tools, high technology and industrial production to provide low quality replacements.
And given that players don't get free logistics and roads the way the AI does, it can even be impossible to shift the supply line to a detour, so by the time you notice and can do something about it to clear a blocked road it can be far, far too late.