Is the implication of being mistreated by those to whom one has shown kindness a sign of God's wrath, and is it necessary to stop being kind to others to avoid sadness?

Calamities do not necessarily indicate Allah's wrath. A person may be afflicted with some of them due to their sins, and they must constantly renew their repentance and seek forgiveness. A Muslim should do good and not cease doing so because of ingratitude or harm from others, awaiting Allah's reward thereby. The Sunnah and the actions of Abu Bakr Al-Siddiq (may Allah be pleased with him) have shown the virtue of continuing to do good even to those who do wrong, in the hope of Allah's forgiveness.