"His spirit was broken" - the basic idea is that people have a certain drive or energy that makes them seek achievement, accomplishment, fame, wealth, success, love, whatever. For a warrior or athlete, this is referred to as "a fighting spirit". Metaphorically, everyone can have a "fighting spirit". Even someone who is paralyzed may have a "fighting spirit" to continue living as best as he/she can despite his/her physical challenges. Another word often used to describe this kind of spirit is "will" as in "a will to win" or "a will to succeed". Some people have incredibly strong "fighting spirit" or "will to win". This is often referred to as an "indomitable fighting spirit" meaning "a spirit that cannot be broken even in the face of great adversity or defeat". These are people who pick themselves up after a setback or defeat and try again. However, every person has a limit beyond which they can no longer persevere and will give up the fight. At this point, one would say "his spirit was broken". Examples: 1) In taming a wild horse, you must teach him to submit to your will but you must take care not to break his spirit. 2) The boy kept wooing the girl but his spirit was broken when he learned that the girl didn't even know his name. 3) The soldiers defended against multiple infantry attacks but their fighting spirit was broken when they saw the tank column approaching.

Use "make a time to meet with you" or "make an appointment to meet with you". These are much clearer and less awkward. "Fix up" and "date" have several meanings, so that part of your sentence is vague.

We need to schedule a time to meet because you are so busy. We need to set a date because you are so busy. If someone's spirit is broken, something caused them to feel really bad.