Frozen Mallet is not a cheap item.
A lot of the gold you are spending on a Frozen Mallet is because of the fantastic passive of snaring targets on hit.
However Ashe already has an infinite snare that is much better than this, so essentially you are wasting terrible amounts of gold for just FLAT HP.
If you want more survivability you have much better options. Not in order of importance:
a) Banshees Veil - if enemy team has serious nukes or stuns (Ryze, Annie, Nunu, EZ, Sion, etc.)
b) Warden's Mail - If enemy team has a lot of auto attackers (Ashe, Tristana, EZ, Corki, Yi, Garen, etc.)
I like Warden's because its passive is that when you get hit, they get snared and also lower attack speed. As Ashe you will find yourself running away from someone plinking at you very often, this guarantees your safe retreat to a more advantageous position in the fight.
c) Leviathan - if you feel you will be getting kills/assists, are low on cash and plan on not dying.
d) Warmog's - if you are being singled out every fight, this makes them want to target someone else cause your health bar gets very very fat. And the advantage is that even though you do less dmg, you are able to actually participate the ENTIRE fight! Wowzers an ashe that lives till the end of a teamfight and got to snare every priority target for her team to pick off! Ludicrous!