I got the same issue of the "repeat at punch point" (as it is named in some music apps) with my new iPhone 5s and iOS 7.0 but it disappeared.
However, I got another problem since the first day and that is still there, after restarting the device and even after updating to iOS 7.0.1...
I would like to know if someone can reproduce it:
1) Start a song with the "repeat one song" option activated
2) Lock the screen with the physical lock button on top of the iPhone
3) Press the same button again
4) You will see the song playing with the progress bar "progressing" (!) on the locked screen. Now slide this progress bar to the end of the song...
In my case, the song re-start at 0:00 but the progress bar will be stuck at the end of the song even if I lock and unlock the iPhone again and again. The song will play normally, the other progress bar of the player app will function normally but the only way to free the progress bar of the locked screen is to move its cursor to any other part of the song.
And you?
Thank you for taking time to try it on your device!