This issue has been noted in the past it seems although it was not a common one.
You say R4- I do seem to recall some issues with deufeufeu's rebuilding method and the a handful of cards with similar issues to what you detail being the symptom (deufeufeu's rebuild method was very accurate but it did not play well with some cards). The fix amounted to rebuilding the ROM with ndstool- you can download ndstool from
http://filetrip.net/nds-downloads/utilities/download-nintendo-ds-rom-tool-ndstool-1501-f29352.html
commands to be run from the command line with the patched ROM in the same directory
Code:
ndstool -x *.nds -9 arm9.bin -7 arm7.bin -y9 y9.bin -y7 y7.bin -d data -y overlay -t banner.bin -h header.bin
ndstool -c jusrebuilt.nds -9 arm9.bin -7 arm7.bin -y9 y9.bin -y7 y7.bin -d data -y overlay -t banner.bin -h header.bin
The first command will extract it and the second will rebuild it. If you prefer a GUI to the command line you can get something like dsbuff to do the same thing
http://filetrip.net/nds-downloads/utilities/download-dsbuff-v1-final-f3100.html