I noticed this in game #157170980. I would play Harbor Village then Taskmaster to get the +1 coin and buy something worth $5, but then my Taskmaster wouldn't stick around for the next turn. Did I do something wrong?
What you described is how it is supposed to work. I looked at the game but I didn't see the problem.
Early on (and turn 9) you often had only $4. Once you bought Piazza for $5, but that is a Projekt, not a card in the strict sense, so doesn't count for Taskmaster.
Also note that gaining Stables with Kind Emporer is a good tactic to keep existing Taskmasters in play, but it doesn't help with newly played ones. That's because the $5 card has to be gained after the Taskmaster is played.