Ok, there is a thread for other demigods that stop attacking their targets after a special ability... I should know, I just posted over there! So please, don't confuse that issue with QoT's auto attack [BUG]!!!
This one is pretty miserable... talk about kicking a dog when it's down... as if QoT didn't already have enough trouble killing enemy DG's, she can't even chase if she wanted to!
Here is the test that I did: I played as oak vs. QoT - I was oak. I battled QoT to the point that she wanted to run. We both have a speed of 6.0. I was able to auto attack her as she ran away, and since the AI runs at maybe 400 health to start, I chopped her down a little past the first enemy towers on exile.
Next I reversed this, and here's what happened: first off, the QoT will sometimes, while auto attacking a DG that standing still, start attacking grunts or minions that are nearby. Ridiculous!
Now, if you do somehow manage to make the enemy DG run, QoT will attack minions or grunts behind her as she runs. She will send attacks at nearby towers. Hmm, actually, that starts to add up, because the enemy DG can run all the way back to their base because, evenly matched for speed, QoT will not be able to auto-attack the fleeing DG!
Her Auto attack behavior is unserviceable, and clearly this is different than the loss of a target after a special ability. This needs to be fixed.