Establishing Safe Operation Range for Lipo Battery with Buck Boost Converter
The regulator you listed may continue working down to 1.7 volts - that is its UVLO level so, adding a diode in series with the power rail to the device is not going to work AND, the diode will represent a big power loss in normal operation because it's conducting power supply feed current. This defeats the object of using a switching regulator in many ways.
Instead, use a comparator circuit and resistors to turn off the EN input when the voltage drops down to 3.1 volts. Here's the sort of circuit that would work to protect the battery: -

Taken from this article subtitled &quot;Li-Ion Battery Undervoltage Lockout&quot;.
You don't have to use SW1 to directly turn the battery off to the TI chip because you can flip the inputs of the comparator and drive the enable pin directly. Or just use it as it stands with a P channel MOSFET.
Version with inputs flipped - note that R4 moves also: -

Simulation

Note that R1 has changed to 4.9 Mohm to make this operate correctly around 3.1 volts: -

I'm varying the battery voltage between 2 volts and 4 volts (blue trace) with the  comparator output (red trace) flipping accordingly around 3.1 volts.