Control Board ohms

My AC has been blown a few transformers, so obviously there is something wrong in the units. I have tested all the control wires for shorts, and the fans, blowers, switches and coils for shorts. Nothing reads below 500 ohms, except for the 24v power leads to the board, that reads 9ohms. At 24v/9 ohms that about maxes out the transformer. So I guess my question is.. Is 9 ohms a bad reading at the control board and can there be a short in the board that still lets the system run but burns out a transformer in about 10 days? Oh and the control board does not show any bad error codes.
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