Is the statement, "I will not advise so-and-so because I assume, based on my knowledge of him, that he will not respond," considered an assertion of knowing what is in his heart, and does sin result from it?

Basing your opinion on your past experience with someone is not claiming knowledge of the unseen. However, a preacher should not despair of people's guidance. Rather, he should advise them, seek Allah's help, and ask Him to guide them, for the hearts of the servants are between two fingers of the Most Merciful; He turns them as He wills. This is similar to what happened with Abu Hurairah's mother, when the Messenger of Allah, peace and blessings be upon him, prayed for her guidance, and she embraced Islam.