I am designing a 7.4 V/2Ah lithium polymer battery operated device. The power switch (single pole single throw) is in series with between the battery. On turning on the device abruptly the device rarely turns on, If the switch is slowly turned on, it powers on almost everytime. The device works perfectly all right with DC sources like an adaptor.
I suspect this is because of the internal over current protection feature of the lithuim battery.
You may try to install a decent low-ESR electrolytic capacitor in parallel with the battery, so if you suspect that the battery for some reasons limits the inrush current, on power-on the cap should help to deliver what’s required ..
The reason capacitors can be used is often because of their quick discharge ability ..