For security reasons, Amazon only lets you download the keypairs only once. So in cases where you lose access to your key pairs, what you can do is, replace the keypair but you can do that only if you stop the instance.
All you have to do is, stop the instance, detach the root volume(only if the root volume is EBS) and attach to other instance for which you have a keypair, modify the authorised_keys file and move this volume back to the original instance.
You can also check out this AWS documentation for connecting to your instance if you lose your private key.