Well, there are two ways around this:
First, you give yourself access to your clients’ accounts by adding your Google Account as a user of theirs.
This way, you’ll see their Google Analytics profiles in your DashThis account. This might be simpler if you create Advanced Segments that are used for many clients.
The second option would be to add each client’s account one after the other. But you’ll have to connect for each one individually.
Once they are added, there is no need to log in again. The operation on linking Google Analytics accounts into DashThis is required only once.