In the readme for this translation it mentions the lack of traditional on-cart SRAM saves. It explains that to save your game you either need an obscure Japanese peripheral (ASCII Turbo File) that plugs into the expansion port on the Famicom or an emulator that supports it.
However I noticed that when playing the untranslated Japanese version of Ninja Rahoi! in Nestopia it was in fact creating an SRAM savefile, while the translated version did not. I got a little suspicious so I checked BootGod's website and, sure enough, Ninja Rahoi! does indeed have a CR2032 battery and internal SRAM. It turns out the iNES header in both the latest GoodNES and no-intro sets do not have the battery SRAM flag set. The internal and external Nestopia XML databases do have Ninja Rahoi! listed as having SRAM and since we know Nestopia overrides the header if the database has an entry for a given ROM, and since the translated ROM's hash would not be present in the XML database this explains why the translated game wouldn't save while the original Japanese version would . After enabling the SRAM flag in the iNES header I have been able to save in every emulator that I have tested.
Well, that's certainly interesting, but I know the game uses this Turbo File accessory and not battery backed SRAM. Maybe they're essentially the same thing and that's why changing the header works.
I did some cursory research, and it seems like the Turbo File is optional in most cases... it seems to mostly be used for transferring save data between different games (Wizardry), or creating multiple save slots. I imagine the only time it'd be really required is for stuff that needs more than the usual amount of save data, like RPG Maker.
Really though, making it a requirement to purchase a separate peripheral to save your game in a silly RPG like this? It seems like it would be bad for business.
I'm sure it was just a matter of "well, we're ASCII and we made this RPG, and we already have this peripheral, so we might as well add some support for it, along with the usual battery save".
(If anyone googles "Turbo File" ten years from now and sees this, keep in mind this is all just me speculating and inferring, hahaha)