Voltage value changed after a while at the output of voltage regulator (TPS5430ddar)
A lot of occasions like this are due to requiring a minimum load on the output. For instance the internal FET for this device will always switch on for typically a minmum of 150 ns at 500 kHz. This will always pass energy per cycle through to the output load and if the load doesn't take enough current the output will rise above the designed value.

You say the GSM module takes a peak of 2A but what is the average current consumption when the regulator starts to fail?

For instance, if the load current were only (say) 100 mA (average), using the formula for minimum value of inductor on page 15 of the DS you'd have to choose a value of 185 uH - you have 22 uH and , if 100mA were your average current then your circuit would do exactly what you describe as the current falls below about 1A.