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I figured you were thinking something like that. But you have to understand, that's not a cheap literary device; it's Aslan's nature. Unlike many characters, who are more or less defined as to where they are at a particular time and can be called on to do a given thing, Aslan is the highest authority next to his father, the "Emperor Beyond the Sea." As is often repeated in the stories, "He's not a tame lion." As such, he is often not present (or, as Lucy discovered in Voyage of the Dawn Treader, there but not visible); He comes and goes at will, and is often seemingly unavailable for the critical moments. But he is available, and when the moment is right he does step in.
Unlike the definition of a deus ex machina, his involvement is in no way artificial or forced. In fact his behaviors are at times both highly inventive and surprisingly personal to the characters for a mere plot device. Consider his involvment in Shasta's life in The Horse and His Boy. As he explained to Shasta, he had been closely involved the whole time. It was he who made sure that the two children and the two horses would meet and thus join forces for their hazardous trip, he who comforted Shasta in the tombs disguised as a mere cat, and he who had been concerned with Shasta from infancy, pushing him to shore where he would be found by the fisherman. A deus ex machina, or a mighty and caring guardian?
It would be fair to compare him in some regard to the eagles in The Lord of the Rings; they come to rescue in tight spots, like when Bilbo and company were trapped in the burning trees, yet they did not carry them across Mirkwood. They cannot be brought so low as to come when the dwarves or even Gandalf call them, because they work for Eru Ilúvatar, the deity of Middle Earth (in other words, a parallel to God in most of our monotheistic religions). You don't expect or command them, you just gratefully accept it when they show up. If one could call on Aslan and make him come to help, or whistle and summon the eagles of Ilúvatar out of nowhere, the heroes would become lazy and never do anything in and of themselves. That would be a contrived solution, a deus ex machina.

Aslan! love him! lovely character!