I was thinking about why some people are good or bad at research/art of problem solving. It may have to do with observations which one makes. When you attempt again and again on daily basis, the random observations simply becomes less important than the observation which actually lead to insights. All important observations are related and gets consolidated just like completing a jigsaw puzzle. So trying every day to think about a problem, helps in gaining insight.
Another possibility could to practice to keep on mind in state of tranquility (much less random noise). This will also enhance the relevant observations. Meditation - practice of shutting of all your senses to the extent possible (that is why possibly, for meditation one closes eyes, sits down at one place, no music) and simply observing of what goes in the mind without trying to control it, or simply letting mind watch whatever it want e.g. your breathing, removes the noise in mind. Your observation clarity becomes better. You can see what is normally not visible.
I have found that every student or person who has come in my contact has different ability to observe acquired in earlier period. Thus they have a limitation in their ability to solve the problem, unless they further enhance their observation skill.
One possibility, is practicing the meditation as described above and see if they can push their limits.
It seems that this limitations get created due to learning from interactions with people in surroundings since childhood. Parents (one of the two who is having dominant influence on the kid) transfers this ability as well as limitation. Even siblings will have different abilities depending on which parents has dominant influence.
So, now case study where thought limitation is pushed further by meditation (consequently, less no of days of repeated attempts in gaining insight), need to be observed to verify the above hypothesis.