  We analyze all available RXTE data on a sample of 13 low mass X-ray binaries
with known neutron star spin that are not persistent pulsars. We carefully
measure the correlations between the centroid frequencies of the quasi-periodic
oscillations (QPOs). We compare these correlations to the prediction of the
relativistic precession model (RPM) that, due to frame dragging, a QPO will
occur at the Lense-Thirring precession frequency $\nu_{LT}$ of a test particle
orbit whose orbital frequency is the upper kHz QPO frequency $\nu_u$. Contrary
to the most prominent previous studies, we find two different oscillations in
the range predicted for $\nu_{LT}$ that are simultaneously present over a wide
range of $\nu_u$. Additionally, one of the low frequency noise components
evolves into a (third) QPO in the $\nu_{LT}$ range when $\nu_u$ exceeds 600 Hz.
The frequencies of these QPOs all correlate to $\nu_u$ following power laws
with indices between 0.4$-$3.3, significantly exceeding the predicted value of
2.0 in 80$\%$ of the cases (at 3 to >20$\sigma$). Also, there is no evidence
that the neutron star spin frequency affects any of these three QPO frequencies
as would be expected for frame dragging. Finally, the observed QPO frequencies
tend to be higher than the $\nu_{LT}$ predicted for reasonable neutron star
specific moment of inertia. In the light of recent successes of precession
models in black holes, we briefly discuss ways in which such precession can
occur in neutron stars at frequencies different from test particle values and
consistent with those observed. A precessing torus geometry and other torques
than frame dragging may allow precession to produce the observed frequency
correlations, but can only explain one of the three QPOs in the $\nu_{LT}$
range.
