My mother whose age is 58 years.she had been sick for six months.her hb was 6 and doctor suggested to tranfuse blood and we tranfused three blood bags.and her hb reached to 9 but within a month it again came back at 4?

You need to become extremely aggressive in uncovering the cause of what appears to be possible bleeding or active hemolysis. Obtain a second opinion from an experienced Hematologist ASAP.

She definitely needs a hematologist as she has a condition causing severe anemia or low hemoglobin, commonly seen in chronic bleeding, conditions affecting the marrow and/or involving red blood cell destruction among others. Following the next set of transfusions, she will need tight follow up with the hematologist.