NO$GBA for now assumes that it's a 4Kbit EEPROM save type which isn't nearly as common as 64Kbit EEPROM which Phoenix Wright uses. So therefore, you will see a save file generated, however, it's the wrong size. DeSmuME features an autodetection algorithm, however, that too is not foolproof. Adding 64Kbit EEPROM, 512Kbit EEPROM, and Flash save support isn't the difficulty part... it's the autodetection that's throwing everyone off since, unlike GBA, that information isn't stored in the ROM anywhere.
To summarize, that's why you're getting save problems. As for the self-appointed forum chastiser, find me an example that I've actually heard of and care about... for all the USA games I've tried, I never actually NEEDED it. Haagen Daas No Breyers isn't a game I frankly care about.