Actually yes, you can. In Emerald, you get to rematch the Frontier Brains with their Gold teams after battling for a few more rounds which varies depending on the facility. It is essentially the number of battles you had to get there *1.5, or the amount of battles between their Silver and Gold matches. I'll try to explain a bit in more detail.
In the Dome, you can rebattle Tucker at the end of the 15th tournament (I have done this myself) and in the Tower you'll get to rebattle Anabel on the 105th battle. I would imagine the number for the Palace/Factory would be #63, and #84 for the Arena. I have no idea about the Pike and Pyramid since they are irregular in terms of when you get to battle the Frontier Brains for the first and second time.
As for the Gen 4 Frontier, it is possible but not in the same way. You are not supposed to be able to rebattle the Brains in the same streak but the Battle Facilities (or the Tower at least) loops after 1792 battles (7*256). Thus, Battle #1793 becomes Battle #1, allowing you to rebattle the Brains with their Silver teams at Battle #1813 and their Gold teams at Battle #1841. At least in Platinum. I know about this because I remember reading some old posts about this in the 4th Gen Frontier thread. You can find and read about it
here and for a few posts forward. Though I'm not sure if this happens in HG/SS too, or whether it is limited to just the Tower or if it happens in the other facilities as well. My guess is that it would be different in the Hall at least if it is possible there since it is different in structure compared to the others.