I find the best way to deal with long running, difficult problems is to (1) document what you are doing and (2) prototype as fast and often as possible. That way you have a measurable record of a systematic attempt to tackle the problem. If the team metrics don’t capture that, you have an easy argument to make that they should and a practical way to do so (commits to a readme or wiki or prototype branch are measurable).

It also helps your teammates and managers identify when you are spinning your wheels and need help. As a tech lead/architect, I find prototypes and documentation about a hard problem extremely helpful for identifying when I’ve made a bad technical decision and selected an approach that simply isn’t efficient or workable. Otherwise, it’s hard to distinguish between that and when the individual dev is simply not up to the job.

It’s also much easier to solicit feedback when you’re stuck if you can offer a record of what you have tried.