I’ve checked and, in fact, the issues I had have nothing to do with the number of tracks of a station. So please excuse my post and ignore it.
I’ve come to the conclusion that the problem is that the current model of TF makes industry links quite unstable. You can have a fully working successful chain: wood->goods->city, but you do something: rebuild some track or a station, renew a train, etc. and some cargo packets are lost. The chain immediately drops. It can even never build up again.