Pay attention to as "how-many-times" would you be overwriting your register. Usually the Program memory or EEPROM data memory has certain read-write or reprogram cycle life of 10,000 or more (also called as endurance). Therefore if your rewriting is within this limit you should have no problem. If you are performing multiple cycles in a day, give a thought about the days you can use from such endurance data from the datasheet of the device.
As far as the power ON/OFF cycle is considered, yes it is more likely that the controller may get affected or get damaged seriously to affect the normal functioning.
But today's controllers have various power control and saving modes where you can use SLEEP, IDLE or Deep Power Saving mode and this should work perfectly fine for your need.
I hope that this information will be useful to you.
I understand from the previous answers that you ask if reflashing a microcontroller might damage it after a while. I have been reflashing AVR microcontrollers dozens of times a day for many days without problem. It is quite difficult to reach the endurance limit in a nonindustrial project, usually something else fails before that!