Flat AP runes= NO just NO!
All you have to do is get to level 7+ for Greater Glyph of Scaling Ability Power to get the same amount of AP as Greater Glyph of Ability Power.

Archangel's Staff?! Why? You aren't Ryze and Elise isn't mana hungry unless you spam her abilities recklessly. She really has no mana problem late game. Basically you are spending a lot of gold for an item just for it's AP. You can get a tankier item so that you won't die as much or an item with unique passives/actives that are more beneficial.

You rush tier 2 boots too late into the game. Elise has a low base movement speed so tier 2 boots are needed to help her escape or chase enemies. Cocoon / Rappel is unreliable for chasing and her gap closer in spider form, Neurotoxin / Venomous Bite, has a small range so it isn't very reliable either.

You should build some tankier items or else other Solo Top champs like Rengar will burst her down easy and feed off Elise! Hp from Rylai's Crystal Scepter is nice but it is definitely not enough. Health is not as effective without defenses.