Capitalize "Partnership" when:
* It's the official name of a specific company or organization: "I work for Partnership for the Homeless."
* It's the first word in a sentence: "Partnership is key to success."
* It's part of a title: "Director of Partnership Development."
Don't capitalize "partnership" when:
* It's a general term referring to the concept of working together: "We're looking for a partnership with another company."
* It's part of a phrase that describes the type of relationship: "We formed a strategic partnership."
In short: If you're referring to a specific organization or entity, capitalize "Partnership." Otherwise, use lowercase.