Currently the government can search your private emails without a warrant as long as they have been stored on a third-party server for 180 days or more. The government only needs to show that they have “reasonable grounds to believe” the information would be useful in an investigation.
The government should not be able to dig through personal emails without first obtaining a probable-cause warrant. The current law was written in 1986 when emails were not stored almost indefinitely as they are today.