Yes they do. Especially when the person has in mind that there is life after death.

However this is not a good approach to religion. As a Christian, the Bible say s

"remember your Creator now while you are young, before the silver cord of life snaps and the golden bowl is broken. Don’t wait until the water jar is smashed at the spring and the pulley is broken at the well. For then the dust will return to the earth, and the spirit will return to God who gave it. ......Here is my final conclusion: Fear God and obey his commands, for this is the duty of every person. God will judge us for everything we do, including every secret thing, whether good or bad.

" Ecclesiastes 11; 6 - 7, 13

I do not think that age plays an all important role, although it might have an influence. In my opinion the interest in religion increases when people start searching for meaning in their life. A second factor that might facilitate the search for meaningful religious experience is also facilitated by traumatic life events. People' s life experiences tend to lead them towards reliogious questioning when comfronted with events that are either physically or emotionally/spiritually threatening.

Piet

Very similar to Piet and White's comments, a person's attitude to religion as he/she gets older depends on a list of factors like the person's upbringing, life encounters/experience like disappointments, failures, achievements, worldview, conception of the afterlife, and more importantly the (environment) dominating atheistic and theistic factors surrounding the person's life experiences.

Those who have had 'divine encounter' with God and are able to trace their 'disappointments' to a personal fault, the environment or the 'devil' outside of self often maintain their faith in God. Those who find the whole conception of the 'Divine' difficult to comprehend and still trace their difficulties to the same divine they deny often become less religious as they grow older.

The principal factor here is a 'divine encounter with God', through Jesus Christ of the Holy Bible. Saul of Tarsus had such encounter. He couldn't deny it afterwards. Likewise Cornelius. (See Acts of the Apostles chapter 9 and 10 on Google at Bible Gateway).

i got the results empirically from 978 people.