I read your question and I understand your concern. Generally speaking Propranolol is an effective drug in lowering blood pressure. Like most drugs there are patients who experience some side effects and fatigue is indeed one of its possible side effects (although dosage is low). If blood pressure is at those values it the current regimen doesn t seem effective either. If those values are only at night being normal during the day I would try what your doctor suggests for some days, taking it in the evening, would be better both for blood pressure as well as fatigue. If it s high during the day as well, or switching the time doesn t work, then I see no reason insisting with it, there are several other alternatives to lower blood pressure, whether of the same class as propranolol with less side effects, as well as other classes of anti-hypertensives. Could be a case of needing more than one drug as well. I hope to have been of help.