What is your model remote?
Identify your Apple TV remote - Apple Support
How old is it? Can you estimate the number of charge cycles in its lifetime?
Did you charge it as Apple describes, directly to a computer USB port, or to a USB power adapter in an AC outlet? Other charging methods may not be supported.
Charge the Apple TV remote - Apple Support
The Apple TV box shouldn’t be turning on and off by itself throughout the day and night unless you keep the remote plugged in 100% of the time. That may point to an issue separate from the remote.
You may want to consult with Apple staff about that: Contact Apple Support - Apple Support (Connect with live support).