Why was your synthroid dose reduced? If it was based on TSH levels alone, then you need more test info to determine your real condition. Free T3 would be very important to know. Along with your symptoms and a full range of test results, you might also check to determine your average body temperature, for comparison to the normal of 98.6. Once you have enough info, you might have some success at getting your doctor to prescribe adequate med. to relieve symptoms. If your doctor wants to prescribe thyroid med. strictly based on TSH, and keeping your TSH level in the middle of the .3-3.0 range, then you might have to find another doctor.
Sounds like it could be the lower dose. You might need a dosage in between or alternating between taking the higher dose oe day and the lower dose the next. You could ask your doctor about this if the fatigue continues. Another thing you might want to do is get your free t3 levels taken. Low free t3 levels could cause fatigue.