MCU on custom PCB suddenly stop working
Assuming batt/MCP73831 is 4.2v, the TPS7361's R9 and R4 produce an output of 3.0v so this is Vdd. If PWR_OFF were an output (either state) while S1 were closed, even for an instant - that is a direct path back to the battery (4.2v, 1.2v more than Vdd.) 

Edit: The STM32L152RBT6 does have many 5v-tolerable inputs (and no \$V_{DDIO}\$ pin to limit this), of which PB12 (pin 33) is one. So what must have happened is, the button was pressed while the micro was asserting an output on this pin, then more current than was allowable flowed into the device (from a pin higher than Vdd.)

Section 6.2, table 11, Absolute maximum current ratings, shows \$I_{INJ(PIN)}\$ is limited to -5/+0mA. My guess is that pressing the button while the output was asserted happened, and the chip failed from an over-current condition.

I'd use a mosfet or BJT to pull EN low instead of pulling the line directly from an output. As @Chris says in the comments, it may be possible to cut a trace and splice in an alteration, but this part of the circuit needs some more thought.