Someone else may be able to give you an 'absolute stopping point', but I really play it by ear if there's something that looks relevant and good, then I'll try and get a link.
I obviously wouldn't put as much effort into getting a link with a lower PA/DA as a high one. If I was to put a lower limit, I'd always use domain authority rather than page authority as this to me is a much better indicator, especially if you're looking for a link on the site in general, not just specifically on the same page as your competitor's link.
If I was to use a lower limit, I'd probably stick around the 40 mark for domain authority to be worth putting time and effort into getting a link, but I would still consider a lower DA if the link was relevant and fairly easy to get.

