For the past 3 years that I have been doing programming contests, I've noticed the trend that I very rarely solve problems in the last 1/6 to 1/5 of the given time in any competition (e.g. last 20 minutes of a CF round or last hour of an ACM event).
Sometimes this lack of efficacy is due to not knowing a niche technique, or running into a genuinely hard problem. However, more often than not, I open the editorial and groan at not seeing a solution that I was millimeters away from on pen and paper. I have never went into the home stretch thinking I would not solve anything (so I don't believe its my mental at fault), but I would like to figure out if there is a way other than straight up practice that more experienced coders use to make the most of every minute of competition.