What are all the possible causes of breast soreness when breastfeeding? I don't want to stop.

Frequency, mastitis. Soreness might be due to doing it too long, or from use of a pump. But apparently the main issue is mastitis, or inflammation of the breasts. This can be from not improper technique of breastfeeding, or from not doing it early enough. Puerperal mastitis can be from infectious inflammation and abscess caused by pathogens like staph. Aureus, strep., and e. Coli. Feeding more often can even help.