There is a burst of energy required when the WiFi transceiver begins operation. You, as many of us, discovered the magic moment that it happens.

Not knowing your circuit I can only speculate. As such, you may get past the burst point with a "large" amount of capacitance across the power input and ground. Using an expansion dock (which you are not) I'm using a 470uF cap just downstream of a 5V regulator just at the +5/gnd dock inputs (there's actually a small cap just upstream of the regulator as well). This has apparently "solved" my problem, however occasional brownouts occur putting the system in the dreaded 3 byte/4 byte reboot issue (another big topic on the forum).

Try a cap and see if it helps. Additionally reduce inductance (wire length) between the power supply and O2. If those don't help, you'll need a new power supply.