Latching power with LDO enable pin
One reason you may not have seen circuits like this is that most designers would use a dc-dc converter rather than a linear regulator, in order to get the most energy from the battery. 

In any event, I do see some problems. First, there is no mechanism for the microcontroller to pull the EN pin low and shut down the LDO. The way you have arranged the diodes it is only possible to drive the EN pin high. You might be able to use a resistor in place of D2, but that would have to be chosen carefully using information that you haven't provided.

When the microcontroller is driving the LATCH output high, to 3.3V, the voltage at the LDO's EN pin won't be higher than about 2.6V (if you keep D2). No way to know if that is a high enough voltage without a link to the LDO datasheet.

When the pushbutton is pressed you will be applying the full battery voltage to the microcontroller's SENSE pin, admittedly through a 10k resistor. Be careful not to damage the microcontroller. Did you intend to make a voltage divider with R1 and R2? R1 doesn't seem to have any purpose.