Sourdough starter - when do you give up?
Typically you can begin to give up at around day 5-7. (Especially if you've taken an aggressive feeding schedule.)

With an aggressive feeding schedule (2-3 times daily), you should begin to see bubbling and sour notes by day three (and is a good indicator for collecting the Lactobacillus bacteria).

Ref: Full Proof Baking

By Day 5, I typically give up if there's no rise or sour notes.

There's two common factors that make sourdough fermentation difficult.


the Type of flour 


  If you use plain/white, there's not enough nutrients - so adding rye, ground cereal, or anything with whole grains will help.

The water quality 


  Chlorine or other chemicals might be present in your source, so getting a tap filter and boiling/resting the water will assist.



Summary:
- try increasing the feeding cycles until you get the sour notes, keep note of the water/flour until you get some smell/reaction.