If I’m subject to the alternative minimum tax, do I lose the benefit of deductions taken on Schedule E for my rental real estate?

No. The computation of alternative minimum tax (AMT) starts with adjusted gross income from which itemized deductions other than miscellaneous itemized deductions and state and local taxes are subtracted (there are certain adjustments to this). Then the result is increased by certain tax breaks. However, no adjustments or tax preferences result from rental real estate activities (other than a depreciation differential, which is the amount that differs for regular taxes from the amount allowed for AMT purposes).