You need to save it in the main menu.
But PS3's RetroArch keeps other settings without even saving the changes in the main menu.
EDIT: Now, after deleting PS3's RetroArch, downloading it (from Brewology, since the last time it was available in RetroArch's official website was in 2020 [it was the 1.9.0 version and it appeared by the name "PSL1GHT", as well as some previous versions]. Since then, RetroArch's official website says "Coming soon" in the PS3 section), reinstalling it, running it, loading a ROM, loading a core, changing its "Aspect Ratio" setting and loading another ROM with a different core, it kept the previous "Aspect Ratio" setting so I didn't have a white screen but when loading ROMs with the Gearboy core, the console returns to XMB, and when loading Pokémon Emerald, it doesn't let me choose the core and automatically chooses the VBA Next one.
EDIT 2: I tried PS3's RetroArch CE (unofficial beta updated 2022-03-15), and after loading ROMs with the Gearboy core a few times, the console didn't return to XMB, and when loading Pokémon Emerald, it let me choose the core I want to load.
EDIT 3: It seems PS2's, PSP's and PS Vita's RetroArch are unauthorized ports according to the official RetroArch website (which still also says RetroArch is "Coming soon" in the PS3 section [it does it for years] and that in the meantime unofficial versions of it are available elsewhere).