Oh this is weird, I know it's not recommended that you go very far away while you're running it but maybe try posting the question in the profile thread to get an answer from the developer.
For the Level 15-50 quest profile, is it meant to halt all quest progress until the Duty Finder lvl15 quest Sastasha is completed? I figured it'd just continue on to other quests. Waiting ~30 mins for a DPS to get queued to the dungeon seems counter intuitive.
As tiesto said, this is intended - it's how SquareEnix designed the main scenario questline. Maybe one day we'll have a Duty Bot botbase to handle this automatically (although is very risky due to interacting with other players directly). For now, as the profile says in the log when it stops. Please complete the Duty it mentions, then start the profile again.
With 15-50 profile, the bot will always stop when you discover new Dungeon - so you need to do it manually. I think it is because they are part of the story line quest?.... I am at lvl 40 atm. Going well but a lot tweaking. Once you get your first lvl 50, things should be easier, lvling via fates is not kind of reliable, depends on zone. I am putting my avatar to a zone below my lvl, so if I am lvl 40 - he is doing lvl 30-35 fates. (he is doing fates while I am not behind my PC) When I am supervising my PC I am doing quests and he gets stuck most of the time.