  In this paper we discuss the production of a heavy scalar MSSM Higgs boson H
and its subsequent decays into pairs of electroweak gauge bosons WW and ZZ. We
perform a scan over the relevant MSSM parameters, using constraints from direct
Higgs searches and several low-energy observables. We then compare the possible
size of the pp -> H -> WW,ZZ cross sections with corresponding Standard Model
cross sections. We also include the full MSSM vertex corrections to the H ->
WW,ZZ decay and combine them with the Higgs propagator corrections, paying
special attention to the IR-divergent contributions. We find that the vertex
corrections can be as large as -30% in MSSM parameter space regions which are
currently probed by Higgs searches at the LHC. Once the sensitivity of these
searches reaches two percent of the SM signal strength the vertex corrections
can be numerically as important as the leading order and Higgs self-energy
corrections and have to be considered when setting limits on MSSM parameters.
