TPS61299: Output peak Current with 2-3V input

Hi,

We are considering the use of TPS61299 for our product and I have tested the TPS61299EVM-103 with our load and it seems to work fine.
But in the datasheet it is written that the chip can output 500mA with 3V to 5V input and limit input current at 1,2A. 
Here is the typical current consumption of our load powered with the TPS61299, measured at it output (input 3V, output 3,3V):

But our product is battery powered and the voltage can decrease up to 2,15V, so it will draw more current.
Here is a current peak seen at 2,15V input.


Is the component able to sustain such current call ? 
Should I use the TPS612997 instead ?
Our goal is to have a really low current consumption in ultra low charge load (2µA), but be able to work with such current peak.

For the ultra-low charge load, we are really happy of the result with the TPS61299 on the TPS61299EVM-103.
Thank you beforehand for your answer.
Manoel