I understand that when blood flow has been cutoff to the spleen it is a splenic infarction. how long can one live with this if no surgery is done?

It's not fatal: You can infarct whole chunks of your spleen and it'll grow back; the infarct ends up as a little white shrunken divot. You won't know it's happening. Infarcting the entire spleen is unusual except in sickle cell disease, where it's usually gone in childhood with most folks none the worse apart from being more vulnerable to pneumococci (get immunized) and other bacteria (be vigilant).