We present quasi-simultaneous radio ( VLA ) and X-ray ( Swift ) observations of the neutron star low-mass X-ray binary ( NS-LMXB ) 1RXS J180408.9 - 342058 ( J1804 ) during its 2015 outburst . We found that the radio jet of J1804 was bright ( 232 \pm 4 \mu Jy at 10 GHz ) during the initial hard X-ray state , before being quenched by more than an order of magnitude during the soft X-ray state ( 19 \pm 4 \mu Jy ) . The source then was undetected in radio ( < 13 \mu Jy ) as it faded to quiescence . In NS-LMXBs , possible jet quenching has been observed in only three sources and the J1804 jet quenching we show here is the deepest and clearest example to date . Radio observations when the source was fading towards quiescence ( L _ { X } = 10 ^ { 34 - 35 } erg s ^ { -1 } ) show that J1804 must follow a steep track in the radio/X-ray luminosity plane with \beta > 0.7 ( where L _ { R } \propto L _ { X } ^ { \beta } ) . Few other sources have been studied in this faint regime , but a steep track is inconsistent with the suggested behaviour for the recently identified class of transitional millisecond pulsars . J1804 also shows fainter radio emission at L _ { X } < 10 ^ { 35 } erg s ^ { -1 } than what is typically observed for accreting millisecond pulsars . This suggests that J1804 is likely not an accreting X-ray or transitional millisecond pulsar .