Sometimes it can help to look at things in a new way.
I was talking with a friend of mine today and he always challenges me to look at things in a new way. It can be frustrating--I say the sky is blue and he'll say "no, it's green." Well, he's not quite that contrarian, but he does always push the buttons. The best time to call him, of course, is when things look bad because if you say things look bad he'll reflexively say "things are great." And what can be better than to be reminded of that at moments when we're focused on the difficulties in our lives? He can be frustrating as hell, but I learn a lot from him. He calls people who cause frustration "zen masters" because of the lesson that you can learn if you approach that person in the right way.
This mirrors an anecdote told by my yoga teacher--I don't remember the details really, but the gist of it involved an old man who had caused someone frustration and how they had realized, through the encounter, the importance of accepting others. After all, what really could we want to learn more than to deal with difficulty with equanimity?
New perspectives can be hard to assimilate; they can be frustrating because they don't match your own vision. They often seem unreasonable. But what a great value they have. Especially if you're stuck on a project. Often being stuck is a result of perspectives that are inhibiting progress; what better way to resolve the problem by working with a new perspective? And not all new perspectives are radically different; some significant changes can be subtle.
It might be argued that getting stuck is caused by a failed perspective. You say "this is the way to proceed." But that means of proceeding doesn't move you forward, and you end up in the same position you were the day before, or worse.
I believe in persistence. I believe that sticking to the effort, and trying to move forward even when there seems to be little progress, are necessary to complete a difficult process. But that doesn't mean that learning during the process is out of the question. We should try to learn as we go, to refine our understanding of what we do, and to refine our ability to do it. Edison said it was 99% perspiration. But that doesn't mean that from trial to trial he didn't try new things. Yes, he was working towards a single vision, perhaps. But he also was refining his process from attempt to attempt; each attempt necessarily suggested new ways to try and things to adapt and change in order to accomplish the desired end.