Japanese maple turns brown when ever it is subjected to excessive sun or dry soil conditions or when the roots or burned by an over application of fertilizer. Try to keep the soil evenly moist and if you are plant is in too much Sun consider moving the container to a very bright shade with perhaps a little morning sun.
Since you're plant is in a container I suspect they cause is a lack of water since plants in containers dry out much more readily than those in the ground do.
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