We present radial velocity measurements of a sample of M5V - M9V stars from our Red-Optical Planet Survey , ROPS , operating at 0.652 - 1.025 µm . Radial velocities for 15 stars , with r.m.s . precision down to 2.5 ms ^ { -1 } over a week long time scale are achieved using Thorium-Argon reference spectra . We are sensitive to planets with m _ { p } sin i \geq 1.5 M _ { \oplus } ( 3 M _ { \oplus } at 2- \sigma ) in the classical habitable zone and our observations currently rule out planets with m _ { p } sin i > 0.5 M _ { J } at 0.03 AU for all our targets . A total of 9 of the 15 targets exhibit r.m.s . < 16 ms ^ { -1 } , which enables us to rule out the presence of planets with m _ { p } sin i > 10 M _ { \oplus } in 0.03 AU orbits . Since the mean rotation velocity is of order 8 kms ^ { -1 } for an M6V star and 15 kms ^ { -1 } by M9V , we avoid observing only slow rotators that would introduce a bias towards low axial inclination ( i \ll 90 \degr ) systems , which are unfavourable for planet detection . Our targets with the highest v sin i values exhibit radial velocities significantly above the photon-noise limited precision , even after accounting for v sin i . We have therefore monitored stellar activity via chromospheric emission from the H \alpha and Ca ii infrared triplet lines . A clear trend of log _ { 10 } ( L _ { H _ { \alpha } } / L _ { bol } ) with radial velocity r.m.s . is seen , implying that significant starspot activity is responsible for the observed radial velocity precision floor . The implication that most late M dwarfs are significantly spotted , and hence exhibit time varying line distortions , indicates that observations to detect orbiting planets need strategies to reliably mitigate against the effects of activity induced radial velocity variations .