You have to work up to it, of course. I don't know how old your child is, but when I was in elementary school I also probably could not have focused on a problem for hours. When I was in middle school I had a long (45 minutes) and boring bus ride and would often spend the entire ride thinking about some problem I was trying to solve. By the time I was in university I could sit and think about a problem for 3 hours (the length of one session of the Putnam exam) without much trouble.
And of course, you (usually) don't have to literally sit! I spent many lunch breaks in school pacing around thinking about problems.
One challenge is the amount of distractions today (internet, devices, etc.) seem to have greatly shortened children's capacity to 1) handle "boredom" in creative ways (like trying to solve a problem, as per your experience) and 2) have the sufficient attention span to see things through. (I used to spend hours as a teen doing math problems on my own because I enjoyed it; but this was pre-internet and my parents didn't even have a TV (out of principle). There was only books, math, and my bike. I feel like kids today are at a huge disadvantage.
And of course, you (usually) don't have to literally sit! I spent many lunch breaks in school pacing around thinking about problems.