Sketch on Mini w/328 only runs once

My UNO board has a pin map just to tell board pins from 328 pins.

All '328P use the same pin map, if you look from the bare die to the software name:
PORTD0,1,2,3,4,5,6,7 = D0,1,2,3,4,5,6,7
PORTB0,1,2,3,4,5 = D8,9,10,11,12,13
PORTC0,1,2,3,4,5 = A0,1,2,3,4,5,6

That's all the software cares about.

There are then connections from the PORT to the physical pins, which is the mapping you see on the schematics and which a board designer carries about.
For writing code and making connections:

byte pin8 = 8;

digitalWrite (pin8, HIGH );

will show up at the header pin labelled D8 on both an Uno and a Promini because in both cases PORTB bit 0 is being addressed, as an example.