If it's picking the second string then it sounds like placement is correct and the twine disc is OK.
How long are the tails on the knot? Which end actually has the knot tied in it? Does it pull the string from the holder on the twine disc or break the string off?
IF it's got short tails on the knot... it's possible that the knife/stripper is not set quite correctly and the knife is too close to the billhook. If so... the tails are cut too short and when they get wiped from the billhook then the knot comes undone.
If it's pulling the top string from the holder or breaking it off then you need to adjust the holder a little bit tighter until it holds it or take a look at the twine tension...