Nothing like trashing ones own theories eh? Apparently, I was wrong (again).
I upgraded my port in Halicarnassus into a Shipwright. It used to trade with Athene for textile only, giving me about 600 income a turn.
When I upgraded it, I went trading with another town (Larissa) for Olive oil. But the original Athene route is now not giving money anymore (and blinking). So it is not based on resources, since these are different resources, and it were the only resources that the ciy exported.

So although once again the totals add up like I described before, I again have no facts about why some trade is blinking and not giving money.
The only thing I can now think of is that a town needs a certain population to manage another trade route, and it uses labour from the lowest income giving up. This would mean that once a town is grown, the blinking should stop (unless the demand for the product rises with the same amount). This would explain why upgrading a port sometimes give blinking trade immediately, and lower incomes (since the lower gets preferred, and there is not enough labour, you'll loose some income) But I can't really test this, and it seems a bit silly to me.

Other then that, I have no idea what it could be. I'm going to continue with my campaign, and maybe later in the game (when I have more towns) try to figure it out with some more experiments.