If multiple lymph nodes are swollen for months on end, what could be the culprit?

Multiple causes: Lymph node swelling represents some type of chronic irritation activating the lymph system. It could be an infection, a foreign body, an allergy, or an abnormality of the lymphatic system itself. Best to be evaluated as you may need a lymph node biopsy if there is not another clear cause of this condition.

Need more info: Where are the lymph nodes? How big are they (>1cm can be significant)? Are they tender/painful? Any symptoms or illness when first noted? Any symptoms developed since (fever, bone pain, abdominal pain)? Several possibilities: chronic infection (EBV, HIV, TB etc), malignancy (lymphoma, leukemia), connective tissue diseases (amyloidosis), inflammatory conditions (lupus, poly/dermatomyositis).