Throwing good money after bad

When does one decide that a venture or investment in something has no more hope and decide to call it a day? Quite often, due to pride, or fear or being called a failure, or the unwillingness to let go of something we treasure dearly causes us to want to continue to do something that does not seem to have any upward potential. We also often have the notion, right or wrong, that if we only pray and try hard enough, God will rescue the situation for us.
When we start out on something new, we are full of passion, hopes and dreams. When things don't turn out as we had hoped or expected, we try all means to adapt and change to make things work. In business, we sometimes use the phrase "throwing good money after bad" to describe the decision to invest more money into a money losing venture in the hope of saving it. Sometimes, it is very difficult to decide when the business needs just a little more money to turn to corner, or if putting in more money will just be a waste of resources.
Recently I encountered this principle in relationships as well. How far can a relationship get before it comes to a point that putting in more time, energy, resources will not make it any better. This is especially so if the other person does not respond as expected or hoped. I am reminded that God loved us unconditionally and without limit. Often even as we reject or ignore God, He still continues to love us and wait for us to respond. Are we, as mere humans, expected to love people in the same way? We do not have unlimited energy, physical capability or resources to continue to love without limit. When do we decide that there is no more point to continue and move on and let God deal with it? Or do we stubbornly hold on to it and hope and pray for God to make it better? Tough decisions.