After establishing a session for Exchange Online and importing it.
PS H:\> $session
Id Name ComputerName State ConfigurationName Availability
— —- ———— —– —————– ————
2 Session2 outlook.offi... Opened Microsoft.Exchange Available
If I run the get-mailbox cmdlet it asks for credentials again.
Creating a new session for implicit remoting of "Get-Mailbox" command...
New-PSSession : The WinRM client cannot process the request. Requests must include user name and password when Basic or Digest authentication mechanism is used.
Exception calling "GetSteppablePipeline" with "1" argument(s): "No session has been associated with this implicit remoting module."
So... since you haven't shared any of the commands you've run, it's pretty much impossible to guess. I can try and explain the errors.
The first suggests that your New-PSSession command didn't include -Authentication. The second suggests that, regardless of whether you have an open session or not, the implicit remoting module can't find the session it was created with.
But again, without seeing what you're actually doing, I'm kind of left to my imagination, which isn't all that good.