I am not sure but want to share some thoughts. Kasme is derived at HSS from KDF (Key derivation function), SQN xor AK, CK , IK and SN Id (serving network id) . Serving network ID is provided by MME to HSS in authentication request named as visited-network. I think not in every MS radio contact authentication need to be performed but if MS select different serving network then only authentication procedure need to performed again since a new Kasme need to be generated.
Looking for others to respond or comment.