Depending on the symptoms, all types of headaches can last 24 hours, 7 days a week. I have had migraines that have lasted for weeks. I have probably had tension headaches that have lasted the same, though in the end everything ends in a migraine for me.
I believe it generally depends on the trigger and if you're able to get relief. Are you suffering a headache chronically?
My doctor has named my migraines, chronic resistant daily migraines because they can occur for days and weeks and are resistant to medications.