Have you tried setting it up so GRUB is working fine on the floppy, then issued 'grub-install /dev/hda' with the floppy out
of the drive? If that causes the floppy not to work, there's something going on behind the scenes, that causes the floppy's version to be somehow out-of-sync with a valid bootloader. AFAIK, grub-install shouldn't invalidate pre-existing instances of GRUB; it seems like it's somehow changing something important on the filesystem itself (e.g. the kernel image filename) such that only the most recently created version is accurate.
OTOH, googling (for "grub grub grub grub"
) seems to imply that your BIOS disk autodetect settings may be the cause of this. Presumably, then, grub-install communicates something
to the BIOS that changes its expectations of the device to be booted from. In any event, you can change this by adjusting your settings as documented here