Patience
As simple as it seems, the virtue of patience is still one of the more powerful tools for personal growth. Sometimes directly working on a problem meets with nothing but resistance. In such situations attacking the resistance is rarely your best option. Consider putting the problem on hold for a while and go work on something else.
Sometimes the mere passage of time can help you solve a seemingly intractable problem. Technology will advance. Your knowledge and skills will increase. You may encounter unexpected luck. The need to resolve the problem may disappear. Getting away from the problem may give you a new perspective. Your confidence may increase by tackling some easier problems for a bit. Your subconscious may pop out a solution when you least expect it.
If this sounds like a recipe for procrastination, it is. Procrastination only becomes a problem when you put off working on what’s truly important to you and get sucked into wasting time. But it’s a valid tool when used to incubate a problem to make it easier and more efficient to solve.
When all else fails, be patient.