Op Amp LM358 LED flasher oscillator
The LM358 might swing its output to within 2V of the supply rail on a good day. That means on a 4V supply it might be able to muster 2V on the output. It barely reaches half Vcc in other words. Try lowering the 100 k resistor from the non-inverting input to ground to maybe 33k and see what happens. In effect you are lowering the target voltage which the capacitor has to charge up to to make it switch polarity on the output.

Wording above slightly changed due to an error pointed out by Michael Karcher.