I would first like to say that I am very sorry for what your mother, you and your family are going through. I have first-hand experience with end stage cancer having lost a wife and older sister within the past year.
Secondly, I apologize in advance for commenting very directly and openly to your question. Thirdly you need to know that I am offering a NON-MEDICAL opinion based on twenty years at the bedside in hospitals and as you already know based on my own personal experience.
As you state in your question your mother is suffering from inoperable rectal cancer. The port she refuses may have been a means of providing nutrition and possibly chemotherapy. I assume she is able to receive pain medication orally. It might also be assumed that she is drinking very little if at all, hence the problem finding a vein for transfusion and other purposes. The fact that they were able, up until now, to use her veins says that she is now very dehydrated and in steady if not rapid decline.
Now to your question: What is an average life expectancy for a person requiring transfusions every three weeks if they cease to get them?
If your mother has been transfused every three weeks and has not been receiving adequate nutrition then her anemia is caused by general and increasing illness, lack of energy and inflammation.
Here’s a short comment on ACD (anemia as an inflammatory response).
Anemia of chronic disease, also referred to as anemia of inflammatory response, or ACD, is a form of anemia seen in chronic illness, e.g. from chronic infection, chronic immune activation, or malignancy. New discoveries suggest that the syndrome is likely largely the result of the body's production of hepcidin, a master regulator of human iron metabolism.
What about the timing? Her hemoglobin has been low and dropping for some time. They have likely transfused because of symptoms i.e. weakness, mental confusion, rapid heart rate and the like. Over the course of treatment they have settled on a hemoglobin trigger. The goal is to transfuse before she suffers. If it takes three weeks for her to near the nadir then symptoms should begin a little after the three week point past her last blood transfusion. When that time arrives symptoms will worsen to the point where her organs begin to shut down and she succumbs. The timing is variable but at her age and stage of illness this process is measured in days not weeks once the nadir or lowest acceptable hemoglobin point is reached.
At some point it will be difficult then impossible to administer pain medication orally. Another route must be found. I feel certain you are in discussion with hospice providers. If your mother has resisted a port because she does not want chemo, transfusion or nutrition, perhaps she will accept the port in order to facilitate hospice care. This will allow palliative care to continue throughout the process.
I'm sure one of our visiting physicians or nurses can clarify, correct or add to what I have said.
Best wishes to you and yours.