If a patient shows persistent hgb drop in multiple recent blood draws over an interval of several weeks (e.g., 2g/dl over 6 weeks) with no overt bleeding noted, at what point would you start searching for a cause? what would be the work-up plan?

A drop in hemoglobin over a period of weeks of "2 grams", may indicate intestinal or renal causes. Get a referral to a GI physician for further endoscopic evaluation to determine the cause.

Unexplained drop in hemoglobin warrants that internal bleeding be excluded. See your doctor at your earliest. You may do a fecal occult blood test with a kit you could buy at the drugstore.