Why can't cardinals over 80 vote in the conclave? Is there a reason given anywhere?
The Church excuses them from voting out of concern for the Cardinals themselves. Selecting the Supreme Pontiff can be a great burden of responsibility, and especially so when one is advanced in age. These Cardinals instead take the role of supporting the electors by helping to lead the People of God in prayer during the election.
From Pope John Paul II's Universi Dominici Gregis, on the subject of papal elections:
In the present historical circumstances, the universality of the Church is sufficiently expressed by the College of one hundred and twenty electors, made up of Cardinals coming from all parts of the world and from very different cultures. I therefore confirm that this is to be the maximum number of Cardinal electors, while at the same time indicating that it is in no way meant as a sign of less respect that the provision laid down by my predecessor Pope Paul VI has been retained, namely, that those Cardinals who celebrate their eightieth birthday before the day when the Apostolic See becomes vacant do not take part in the election.10 The reason for this provision is the desire not to add to the weight of such venerable age the further burden of responsibility for choosing the one who will have to lead Christ's flock in ways adapted to the needs of the times. This does not however mean that the Cardinals over eighty years of age cannot take part in the preparatory meetings of the Conclave, in conformity with the norms set forth below. During the vacancy of the Apostolic See, and especially during the election of the Supreme Pontiff, they in particular should lead the People of God assembled in the Patriarchal Basilicas of Rome and in other churches in the Dioceses throughout the world, supporting the work of the electors with fervent prayers and supplications to the Holy Spirit and imploring for them the light needed to make their choice before God alone and with concern only for the "salvation of souls, which in the Church must always be the supreme law".