Well, after killing her own master, I seem to remember Caster's flashback saying that she wouldn't have lasted the night (I think it even mentioned something like after an hour or two she had started to disappear?). On top of that, they need more then magical energy to stay materialized. They need an anchor in this world or else they'll disappear no matter how much magical energy they have, same reason why Assassin was bound to the land at the Ryudou Temple, even though Caster had his command spells.
Also, direct quote from the F/SN Visual Novel:
Quote:
Independant Action: B
Ability that allows independant movement even after the Master's magical energy supply is cut off. With Rank B, it is possible for a Servant to stay in this world for two days after losing its Master.
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I think its pretty safe to say based on that that there is no way for a non-Archer servant to last more then a few hours, let alone an entire day, without a master.