Sivir's Mana Problem

Build Essence Reaver into Phantom Dancer or Statikk Shiv for damage and mana restoration. The more often you crit, the more mana you will restore.

If you are still having issues, consider changing to Meditation from Executioner in masteries.

they gave her mana restoration that doubles as an ability shield. What more do you want

if only she had a shield that gave her quite a lot of mana back... oh wait... also:

No, lower the mana cost then you'd have to increase the cooldowns on abilities.

Otherwise you're forever pushed into tower and sivir + her support can go make a quick roam and return by the next wave.