A solution would be to force the key files to be kept permanently, by adding them in your
IdentityFile ~/.ssh/gitHubKey IdentityFile ~/.ssh/id_rsa_buhlServer
If you do not have a 'config' file in the ~/.ssh directory, then you should create one. It does not need root rights, so simply:
...and enter the lines above as per your requirements.
For this to work the file needs to have chmod 600. You can use the command
chmod 600 ~/.ssh/config.
If you want all users on the computer to use the key put these lines into
/etc/ssh/ssh_config and the key in a folder accessible to all.
Additionally if you want to set the key specific to one host, you can do the following in your ~/.ssh/config :
Host github.com User git IdentityFile ~/.ssh/githubKey
This has the advantage when you have many identities that a server doesn't reject you because you tried the wrong identities first. Only the specific identity will be tried.