What happens when a relationship reaches a stalemate? Thinking back, I had this experience in the professional sphere once. I simply gave up advocating for change with one administrator--there was no winning with her, and it wasn't worth the time or effort anymore. Instead, I pushed my energy in another energy where good work was possible. There was disappointment, but no long lasting bad feelings. It was a good decision when met with a relationship stalemate.
Stalemates can happen in any relationship. Those stalemates can be short lived or long lasting. When that happens, you have to think about what you will do. I think it's a good idea to try many strategies to end the stalemate if the person and relationship are meaningful to you. Then if the stalemate continues after many attempts to move forward, you may have to give the relationship a vacation for a while until a new and better strategy comes to mind.
In the best of circumstances we avoid relationship stalemates by continually nurturing and supporting good relationships with people in your life. Good communication, apt listening, support, and interest in others are simple ways to keep relationships strong. Onward.