A standard AA battery is assumed. Short answer is: revise your expectations.
With an output voltage of 3.4 volts and a load of 5.5 ohms you should get a current of 619 mA and this will translate to a current from the 2.7 volt input of about 900 mA if power transfer efficiences are taken into account (approximately 15%).
When this much current is drawn from an AA battery the terminal voltage drops possibly as much as 0.2 volts per cell and the result of this is that the input voltage instead of being 2.7 volts is now more like 2.3 volts.
With 2.3 volts at the input to the boost regulator, what current can you expect to be taken if the output is sustained at 3.4 volts. It will be more like 1.06 amps and this in turn modifies the the terminal battery a bit more and there is an iterative process that ends up with possibly only 2.1 or 2.2 volts at the input and rapidly the batteries are running out of steam to sustain things.
Given also that the output current of the TPS61025 is about 200 mA (front page circuit of the data sheet), I think you are expecting too much: -