Acts 17:4-5 "And some of them were persuaded and joined Paul and Silas, along with a large number of the God-fearing Greeks and a number of the leading women. 5 But the Jews, becoming jealous and taking along some wicked men from the market place, formed a mob and set the city in an uproar; and attacking the house of Jason, they were seeking to bring them out to the people."
I recall ministering among Muslims years ago. Roughly 30 of us had engaged in public meetings for better understanding with Muslims for two years. Although we saw no converts, we did see a few intellectual objections wither. Apologetics requires patience and prayer. Eventually, there will be conversions. As Paul traveled throughout the Greco-Roman pagan infused world of Macedonia, he did see people convert to Jesus Christ. Again, despite the opposition, such antagonism served as a backdrop to bring into sharp relief the integrity of Paul and his companions in their apologetical task. Sometimes God can use our lives, as well as our arguments to convince unbelievers that what we believe gives confidence in the face of opposition. So, when doing Christian apologetics, expect rejection and expect conversions. But there is one more expectiation...
16 Now while Paul was waiting for them at Athens, his spirit was being provoked within him as he was observing the city full of idols." The one thing we learn about God's Sovereignty is that in His exercise of it among people and circumstances (such an exercise of sovereignty is also called God's providence), God is a very strategic God. What resulted from the combined rejection and reception of Paul's apologetic efforts? God used him and God moved Paul to where He needed him to be. On the ground level it may had appeared that Paul was running into walls and running in circles. However, God was strategically and providentially moving Paul down the entire length of the Macedonian region.
If we can keep in mind that God can use anyone with a willing heart and a big view of Him, then no matter what happens, the expectation of being used by Him will overrule the discouragement from rejection and reinforce patience in prayerfully waiting for conversions.