Yes Gitara died of old age, but Cadsuane is far older than anyone thinks, by at least 50yrs. Her secret is her angreal. Part of their lifespan is also determined by how much they use the power, and with her angreal she is equal to Rand

Yes Gitara died of old age, but Cadsuane is far older than anyone thinks, by at least 50yrs. Her secret is her OP strength. The average Aes Sedai lives about 250, and since she is MUCH strong than average, of course she live longer than any of the others. It's never mentioned, but I don't think the Aes Sedai realize this, which would explain why they keep thinking she should be dead.