Hi & Welcome.
Yes, when used for prolonged duration NSAIDs can cause anemia.
Non-selective COX-1/COX-2 inhibitors (nonsteroidal antiinflammatory drugs) like Mobic (Meloxicam) suppress the pain and swelling by reducing the levels of
prostaglandins which are actually useful in protecting stomach lining from the harmful effects of stomach acid and its blood supply.
So, a decreased level of prostaglandin can result in gastritis, ulcers of the stomach or duodenum causing bleeding.
The chronic NSAID use may present with
iron deficiency anaemia or hypoalbuminaemia due to blood or protein loss, and may develop overt bleeding, perforation, or strictures.
Apart from NSAID induce bleeding, the
chronic kidney disease is also responsible for her anemia. Patients suffering from chronic kidney disease do not produce enough hormone erythropoeitin (which is required for the formation of red blood cells in the
bone marrow) thus resulting in anemia.
So, in addition to taking iron and multivitamins she may also need injection erythropoetin to increase her
hemoglobin level and thus to prevent anemia.
Hope the advice given above would be useful to her.
Best wishes.