why is there current loss
The maximum power you can get from a source depends on its output impedance (please google for "maximum power theorem"). The circuit shown is a boost SMPS. Neglecting any losses, if you have 5V @ 56mA (280mW) at the output and 300mA at the input, your input voltage should be near 0.9V. If the loaded input voltage is greater than this your circuit is lossy. In the shown circuit, losses come from the forward voltage and switching losses of the diodes and the mosfet. Also the inductor may be saturating or having a large series DC resistance. And finally, the controller consumes some power. From this kind of circuit you can expect an eficiency near 75% depending on the input voltage. Remember that, keeping the output power constant, than as the input voltage decreases the input current will increase proportionally.
If 280mW is too much for the solar cells (it depends on the incident light intensity) than you should consider to limit the output current so that the output power multiplied by the eficiency of the circuit is near to the maximum power you can get from the cells. I think that in the proposed circuit this can be easily done by just increasing the value of the inductor.
The maximum output power (from the cells) is obtained when the load equals their output impedance or when the current drawn from them equals Vcell/(2.cell_impedance). So, my suggestion is to limit the SMPS output power to a value that brings the current near to this value. Some compromise must be done because it varies with respect to the incident light intensity.
Regards