Use a slower 555 timer to trigger the faster 555 timer on and off. PWM'ing a PWM signal.
if you want the gap you'd need a third 555. PWM'ing a PWM'd PWM signal =)
The second 555 feeds the reset pin of the 38kHz oscillator 555 so that it is on for 10 cycles and off for 14 cycles. The duty-cycle of the second 555 must be about 10:14.
I am beginning to work on a similar project, and this discussion in very helpful.
One thing I have not seen mentioned is the wavelength of the LED, and the wavelength that the receiver is designed to detect, if those are mismatched it could be causing your problem.