A relationship stalemate can occur when two people see the world in two very different ways. A stalemate doesn't mean that one person is right and the other person is wrong, but instead it means that two people stand so far apart on issues, efforts, and vision, that there's little room for companionship or collaboration.
In the best of circumstances, people like me hope to work with everyone with common values and direction--I like the idea of open, caring collaborative work. Yet, in life, I've had the experience of living and working with people who see life very differently from me, and who are uninterested in the collaboration and openness possible.
While I do not wish for situations like this, I know that this happens. A long time ago I went after situations like this with high energy and perseverance--I wanted to change the other person, convince him or her, and/or find common ground. Action liked this only served to sever ties, so know I've learned to give it time, let people live their lives, and make time to know and honor their work, commitment, choices, and vision more. Eventually with an attitude like this I've found that stalemate becomes respect, understanding, and greater learning and care for one another. This, I believe, is the best way to move forward when a stalemate occurs.