  We identify scenarios not ruled out by LEP data in which NMSSM Higgs
detection at the LHC will be particularly challenging. We first review the
`no-lose' theorem for Higgs discovery at the LHC that applies if Higgs bosons
do not decay to other Higgs bosons - namely, with L=300 fb^-1, there is always
one or more `standard' Higgs detection channel with at least a 5 sigma signal.
However, we provide examples of no-Higgs-to-Higgs cases for which all the
standard signals are no larger than 7 sigma implying that if the available L is
smaller or the simulations performed by ATLAS and CMS turn out to be overly
optimistic, all standard Higgs signals could fall below 5 sigma even in the
no-Higgs-to-Higgs part of NMSSM parameter space. In the vast bulk of NMSSM
parameter space, there will be Higgs-to-Higgs decays. We show that when such
decays are present it is possible for all the standard detection channels to
have very small significance. In most such cases, the only strongly produced
Higgs boson is one with fairly SM-like couplings that decays to two lighter
Higgs bosons (either a pair of the lightest CP-even Higgs bosons, or, in the
largest part of parameter space, a pair of the lightest CP-odd Higgs bosons). A
number of representative bench-mark scenarios of this type are delineated in
detail and implications for Higgs discovery at various colliders are discussed.
