A lot of LDO regulators are very picky with their output capacitors. Often going for a capacitor than what is specifically listed (tantalum 2.2uF) the LDO will be unstable. Low ESR capacitors often cause problems because the added pole of the output capacitor is not "lost" at high frequencies. From the data sheet for the part:
For low-dropout regulators that are stable with ceramic output capacitors, see the μ
Cap MIC5245/6/7 family.
So I would first say try to reduce the output capacitor or be sure all are higher ESR.
