Well, I tested that rom by flashing with neomax 1.5 just now.. I actually can't even get it to run (it crashes during part of the intro). The various other gba roms I tested all seem to save/restore properly. I'm using a neomax 512 flashcart, which is similar to your Neoflash.
That default save location should always show up. Every time I turned off my ds and turned it back on after saving in-game, it would ask me if I wanted to back up the save. Selecting 'ok' seemed to back up automatically to the default location (the name stays the same). Then, I just ran the rom again and easily restored my save point.
You can also create additional save locations besides the default one. Just select the rom, go to the SMS tab, hit 'start' to bring up the menu, and 'create'. This creates a new save game file, which should show up under the default one. Later on, you can select which one you want to use by using the 'load' function (and then run the rom from the menu, and your correct save positions should be present)
If none of this is working for you, have you checked that your battery on your neoflash is not dead?? GBA saves don't function correctly if the battery is non-functional.
As far as the neoflash/magic key 1 being able to backup ds and gba games, I don't think it's very reliable as it's a first-generation product. The magic key 2/3 function better for saving, but even these devices aren't close to perfect, since these are still new products (bugs are being worked out). Sure, xecuter chips for the xbox work perfectly, but that's a mature 5 year old console. The DS scene is still evolving...
You should definitely test other gba roms on your cart to check if you can save/restore. Assuming your battery is ok, many of them should function correctly...
BruceG