You answered it!! Your fuel pump!! Check the fuel pressure at the fuel rail and compare it to specifications. Use a fuel pressure gauge to do this. You are interested in fuel pressure at prime (position before start), fuel pressure at idle, fuel pressure at wide open throttle (goes higher then drops a bit?), and fp with key off (does fuel pressure drop a little and hold?).
Tell us if you have the CPI or TBI engine becuase the fuel pressure requirements are very different.
By clicking the key, as noted above, you are priming the fuel pump. By doing this several times, you are "artificially generating" more fuel pressure. This procedure won't continue to work as the fuel pump will become more and more tired.