I keep getting eczema on 1 of my eyelids. The only thing that helps is cortisone, but only helps for a few days, then it's back. Suggestions?

Identity allergens. I don't know much else to do except see a specialist who could prescribe topical tacrolimus or systemic treatment if indicated.
Good skin care. First, use only hypoallergenic skin cleanser, and make sure you're applying a hypoallergenic moisturizing lotion at least twice daily to all dry or excema-prone areas. Use only hypoallergenic makeup (if any) and makeup remover. If you must use hydrocortisone, get the 1% ointment (ointment works better). If still not enough, ask your doctor about a non-steroid eczema topical medicine. Hope this helps!