AnA buck converter doesn't draw a continuous input current. The problem is that your solar cell is specified at the maximum current it can supply continuously, not the average of a pulsed current. In order to draw a more continuous current you have to add filters at the input of the converter. Once the output draws a little too much current the input drops dramatically(remember a solar cell acts almost like a current limited voltage source). Even better than a filter would be to get the maximum amount of power out of the cell by using a maximum power point tracking charger. The battery will act as a huge filter making it possible for your circuit to draw higher peak currents and to operate when there is less or no sunlight.
Example: In case of an ideal buck converter at high switching frequencies if you convert 10 volts to 5 volts 1A you will draw 1A current pulses at a 50% duty cycle, so 500mA average current. If there is no input filter the input source has to deliver the full output current. Beyond the maximum power point the voltage of the cell will rapidly drop. The converter will try to draw a larger current to compensate for this causing an even greater drop.