Ah I see, yes I have a Kung Fu Flash which explains it! Hopefully you find a fix in the future, in the meantime I'll see if I can complete the game in one sitting :)
From the tests I made, it really looks like the problem is not in the game, but in KFF (that's why I opened the issue of KFF's GitHub). Unfortunately, there hasn't been any reply yet, nor have I received any feedback from EF owners, so I still don't know for sure.
That said, if you send me an email from the same address you purchased the game from and tell me which zone you reached, I can send you a cartridge image which will allow you to start from there.
By chance, I stumbled upon this again, and now I have a different answer. Further tests proved that saving didn't work if the location was in the first 64 kB of the image. The KFF author confirmed that it's a restriction imposed by the firmware. The update released about 11 days works around this issue and now saving works also on KFF.