  We present an update of our analysis [1] which includes additional ensembles
at different quark masses, lattice spacings and volumes, all with high
statistics. We use $N_f=2$ mass-degenerate quark flavours, employing the
non-perturbatively improved clover action. The lattice matrix elements are
converted to the $\overline{\rm MS}$ scheme via renormalization factors
determined non-perturbatively in the RI$^\prime$-MOM scheme. We have
systematically investigated excited state contributions, in particular, at the
smallest, near physical, pion mass. While our results~(with much increased
precision) are consistent with Ref.~[1], comparing with previous determinations
we find that excited state contributions can be significant if the quark
smearing is not suitably optimized, in agreement with other recent studies. The
difference with respect to the value for $\langle x\rangle_{u-d}$ extracted
from experimental data is reduced but not resolved. Using lattice sizes in the
range $L m_\pi\sim 3.4-6.7$, no significant finite volume effects were
observed. Performing a controlled continuum limit that may remove the
discrepancy will require simulations at lattice spacings $a< 0.06$ fm.
