There are two parameters that matter in the boost converter: Duty cycle, and switching frequency. (And a third: whether it's in continuous or discontinuous conduction mode)
You are saying that the capacitor "drains" when you supply the load -- this means that you're not switching the converter fast enough to re-"fill" the capacitor.
The reason for this may be that there's too high resistance in your inductor, or your transistor can't sink enough current (typically, power N-channel MOSFETs are used,) or your battery source has too high internal resistance.
A 2N2222 is not a power transistor. Also, you don't indicate how much current your oscillator will source. Given that you're using a BJT, the amount of current through the transistor is directly proportional to the amount of current out of the oscillator (up to the saturation point of the BJT.) Without knowing more, I would suspect using a higher-performance transistor with a higer switching rate (say, 20 kHz) and a lower-resistance inductor would improve the performance you see.
Also, the schematic shows a sine generator. You want to use a square wave for a boost converter.
Hook up a scope to various points in your circuit, to measure how it's doing, and this will tell you where it goes wrong.