Does the lack of answered prayers to be rid of the sin of looking at forbidden things—despite repentance, acts of worship, and fervent supplications on days like Arafah—mean a lack of sincerity in one's intention?

Every human being makes mistakes, and the best of them are those who repent. So do not despair of repentance, and continue to strive against yourself and repent sincerely every time you sin, even if the sin is repeated. Do not let Satan prevent you from repenting through despair. Increase good deeds that erase evil deeds, and continue in acts of obedience. Take measures that help in lowering your gaze, such as marriage or fasting, and frequently engage in remembrance of Allah (Dhikr) and supplication (Du'a). Associate with righteous people, and adhere to gatherings of knowledge and remembrance. Remember the virtue of lowering your gaze and the danger of letting it loose.