EEPROM-YES games are standard non-NAND games. These should be working no matter what. The NAND games (EEPROM-NO) have savedata written to the SD on the 3DS. Some EEPROM-NO games also save data to 3DS SD. Anytime your game prompts "saving to SD card, please wait" or at beginning "creating save on SD card" the backup of the game itself won't help.
You have to make sure of two thing:
1) When you write the new copy in Diskwriter that you aren't changing the template header IDs. The moment you do this, the game thinks it's a new cartridge and must make new savedata on sysNAND SD.
EXAMPLE: I have Ult NES Remix. I delete it in Diskwriter. I don't do anything to my template but update it to latest version. I re-write to mSD. Still thinks it's athe same game and my savedata works. The moment I insert private headers, savedata is lost because it thinks it's a new cartridge.
2) Make sure your backups aren't old. IE, BACKUP SAVEDATA RIGHT BEFORE YOU CHANGE ANYTHING. Doesn't hurt to BACKUP GAMES. This basically creates a double backup of the savedata. Just in case. If restoring the game doesn't work, write the original .3ds to mSD and then restore savedata backup.
Remember, the Sky3DS is acting like an original cartridge. So any savedata that games creates on the system's SD card will be made. If you use a copy and any of the .3DS file is different from the one before (including template), it won't access the savedata but instead create new.
Best to save in 1.06 THEN transfer to 2.02b1. Please skip 2.00b8. It had formatting errors. So you can try, but no guarantees it'll work.
As for anyone saying 2.00b8 "works fine for me" wait till they update to 2.02b1... gonna open up a can of worms and find out how bad 2.0 was.