I didn't encounter this in my single 2-player game, but now that you mention it there are 8 towers possible in each colour. If every tower reached it's maximum height of 4, then 32 tower pieces would be required for each colour, but only 16 are provided.
I can only assume that the tower pieces must be deliberately limited, and recognising when the supply is running short is part of what players have to watch out for.
Some sort of official answer would be nice though - or at least could someone point out if something is in the German rules but missing from the unofficial English translation?
I don't think I missed anything in the rules, so its good to get a definite answer. Our copy of the game has arrived today and unfortunately our tower levels are even more limited - no black tower pieces at all! Hopefully Hans im Glück will again be as quick to respond.