Yes, cycles repeat themselves. There is scriptural evidence that says this. But there is one change. The 'jiva' that is inhabiting your body in this life is not the same jiva from your life in the previous cycle nor will it be the same jiva in the next cycle. So although your body will repeat its actions, the jiva experiencing 'your life' in the next cycle will be a new jiva whose karma is then suited for birth in your body. Your jiva will have already accumulated new karma and taken birth in another higher/lower body (or your jiva may be in a heaven or better yet attained Liberation).
Swami Vivekananda in Jnana Yoga gives the example of the ferris wheel. The ferris wheel goes round and round and when it stops it lets the passengers (jivas) out of the cars and takes on new (jivas) passengers in the same cars.
The Bhagwat Gita (2.12) says:
"Never was there a time when I did not exist, nor you, nor these kings of men. Never will there be a time hereafter when any of us shall cease to be."
The Bhagwat Gita (9.7) says:
"At the end of a cycle all beings, O son of Kunti, enter into My prakriti, and at the beginning of a cycle I generate them again."
The Brahma Sutra (1.3.29) says:
"And because of the sameness of names and forms (in every fresh cycle) there is no contradiction (to the eternity of these Vedic words) even in the revolving of world cycles, as is seen from the Sruti and the Smriti."
The Vishnu Purana (I. v. 65.) says:
"As in the rotation of the seasons, the very same signs of the different season are see repeated, so also at the beginning of a cycle the various things are created as in the previous cycle."
Rig Veda (but I don't remember the verse #) says:
"The Lord creates in this cycle the sun and the moon as they existed in the previous cycle."
In one of the puranas, in his Boar incarnation, Vishnu turns around and says to the goddess Earth "Every time I carry you this way..." referring to the fact that He has done the same in prior cycles".
This is why some people have the mental ability to foretell the 'future'. It is not so much a case of being able to see the future, it is more a case of understanding the past - the prior cycle. Although they can see the past (or future) of a body, they cannot see the future of your jiva. What you do with your mind in this birth is your own making. You cannot escape the karma of the body you have (Gita 18. 60. 'you shall do even against your own will.') but you can put your mind and heart towards God.
In a certain way, your body is eternal.
The only sure method is to realize God and escape the endless round of birth and death.....