I had the same issue online so I went to AAA to order plates and they told me there are certain combinations of numbers and letters that are not allowed. the online service does not give a reason why it is rejected. AAA told me the combinations that are not allowed but I don't think I have it anymore. I was trying use use 3 letters followed by 3 numbers and vice versa. Those combos aren't allowed. The online site will allow you to go all the way through to payment before it is rejected and doesn't give any reason. I ended up ordering 4 letters followed by 3 numbers and that was OK.
One of the ladies helping me actually referenced a DMV code that specified the combinations that were not allowed. I think its related to some letter and number combinations being for emergency vehicles.
I guarantee this is the reason you are being denied the plates.
I wouldn't count on every AAA service person being knowledgeable about this. The first lady helping me couldn't understand why the plate was being rejected either so she asked for help and the second lady told her about the DMV code.