HETE J1900.1--2455 is a peculiar accreting millisecond X-ray pulsar (AMXP) because it has shown intermittent pulsations after 22 days from the beginning of its outburst. The origin of intermittent pulses in accreting systems remains to be understood. To better investigate the phenomenon of intermittent pulsations here we present an analysis of 7 years of X-ray data collected with the Rossi X-Ray Timing Explorer and focus on the aperiodic variability. We show that the power spectral components follow the same frequency correlations as the non-pulsating atoll sources. We also study the known kHz QPO and we show that it reaches a frequency of up to approximately 900 Hz, which is the highest frequency observed for any kHz QPO in an AMXP. We also report the discovery of a new kHz QPO at ~500 Hz. Finally, we discuss in further detail the known pulse phase drift observed in this source, which so far has no explanation. We interpret the behavior of the aperiodic variability, the high frequency of the 900 kHz QPO and the presence of the pulse drift as three independent pieces of evidence for a very weak neutron star magnetosphere in HETE J1900.1--2455.