Context. Launched in 1996, HSTOF on board SOHO was the first instrument to detect the energetic neutral atoms (ENA) from the heliosheath. After mid 2003, the field of view of HSTOF was restricted to the flank sectors of the heliosheath, in which region the energetic ion distributions are still unknown. Interpretation of these data requires understanding of the energetic ion transport in the inner heliosheath. Aims. We update the HSTOF ENA hydrogen and helium spectra by adding the results from the recent (2006−2010) measurements. We calculate the energetic ion distributions in a numerical model of the heliosheath and use them as a basis for interpreting the HSTOF ENA observations, in particular those of the flank sectors. Methods. The hydrogen and helium ENA spectra were derived from the HSTOF observations of two 90 • -wide ecliptic longitude sectors around the crosswind directions. The energetic ion distributions in the heliosheath were calculated in a simple model of the heliosphere, assuming that the main acceleration occurs at the termination shock. The effects of different processes (charge-exchange loss, adiabatic acceleration, parallel diffusion and escape across the boundary) were determined with different assumptions about the boundary conditions and the transport parameters. The resulting ion distributions were used to calculate the ENA fluxes, which can be compared with the observations by HSTOF and other instruments. Results. The energetic ion density in the flank sectors of the heliosphere is lower than in the forward (upwind) sector. As a result, the contribution of the flanks of the heliosheath to the production of ENA is not directly proportional to the thickness of the heliosheath, but instead is comparable to the contribution of the forward sector, which agrees with the HSTOF data. The HSTOF ENA flux intensity is nevertheless significantly lower than the model calculations. Near the heliopause there appears a region of low energetic ion density caused by the charge-exchange and the escape losses.