One of the most challenging parts of teaching problem solving is encouraging students to not give up. One of the standards for mathematical practice in the Common Core references this:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
I was given a link to another blog with one possible strategy to address this. It’s called the “8Q5” approach. Rather than trying to explain it myself, here is the link to that article: https://problematizingmathteaching.com/2017/07/30/8q5-the-perseverance-project/
Check it out and let me know what you think!