I have noticed that if a town is receiving goods from more than one source, demand can fluctuate between the sources unpredictably.

You might want to go thru some tutorials availabe  in community guides of steam. There is also my “Learning Cargo in 10 mins” tutorial.

Yeah, I did that, and I think I read even the guid by that name, but couldn’t find anything that explained this sudden drop. The line worked perfectly fine for over a century, was well saturated – I adjusted the number of trucks when needed – and then the production simply went away.

Is your town obtaining goods from elsewhere?  Has it any unfulfilled demand for goods?  Don’t forget that goods will only be supplied to satisfy demand.

That’s the weirdest thing, it was the only production facility supplying the goods, and the demand was not fulfilled – it was something like “1/63”. Once I connected another factory, much further away, – it instantly jumped into gear, and the new line was very profitable, too. In another town, the production dropped – not to a halt, though, but it wasn’t fulfilling the demand either, and the trucks were running half empty.

a) See in the factory properties if it says “Line usage:yes”.

b) Turn “Cargo” on in the bottom right menu and see the goods boxes move around.  Sometimes, the go on foot to the city, sometimes the city gets goods from other sources.

c) Check that the vehicles you use can certainly carry Goods.

Hope it helps.