I second Levidian's comment. With two mana-free sources of damage and three healers, you have the potential to outlast nearly every other team out there.
A friend of mine played on a tri-healer setup (Resto Druid, Holy Paladin, Holy Priest) and they played the mana war. Healing through unsynchronized damage is trivial and you have two sources of very heavy mana consumption: Wounding Poison and MS (both effectively reducing healing-to-mana efficiency by 50%). Utilizing that, a drinking rotation, and mana-free damage, they simply won games by draining their opponent mana pools.
If your Rogue is dying too early, particularly to ranged damage, teach him how to use obstacles to break LoS of ranged aggressors. Also, sychronizing a BoP and Cloak of Shadows on the Rogue makes him nigh-invulnerable and he can easily Vanish out to safety. Finally, a pure PvP spec will help increase survivability vastly (e.g. Prep'ed 2x Evasions vs. melee).
Edit- I didn't realize you had a Druid. Innervate and Poison Cleanse will nearly gaurantee you victory over the mana war (as long as you're mindful of LoSing Mana Burns) and the Druid can cheese the shit out of drink + Shadowmeld since he's NE.
Seriously, you should all walk in with 2 stacks of Star's Tears, each get behind a pillar, and mash drink at every opportunity.
Edit 2- If you need to drop a Mana Tide totem and you absolutely cannot drop it behind some LoS obstacle, drop the totem and
stand on top of it. You'll be surprised at how long they last, especially if you're a huge Tauren.