I'm not sure I follow. Are you currently starting Pageant from Task Scheduler? Or are you asking if starting it from Scheduler would make things better? Why Task Scheduler? Just put a shortcut to Pageant to shell:startup.

What do you mean by "permanently"? Permanently for the current Windows login session? Or permanently like forever?

Thank you Martin,
Now I recover the screenshots. Btw do you know if scheduling (e.g., through the task scheduler of Windows) a batch adopting the SSH keys with passphrase to access the server SFTP will grant to save permanently the passphrase? (or I need to insert manually every time?) Indeed I use the command "C:\Program Files (x86)\WinSCP\Putty\pageant.exe" "PRIVATE_KEY_PATH" in the batch to recall the Paegant every time to save the passphrase but it doesn'y seem to work.

When you stop Pageant, the passphrase is lost. That's how it works.
But disconnecting session in WinSCP should have no effect on Pageant. Please post a screenshot of Pageant window before and after disconnect.

Hi, I have an issue with the Pageant of WinSCP. When I save the private SSH key on Pageant with the passphrase, this one remains saved only for the current session. Every time I disconnect from my server or Pageant is killed with a forced stop, I have to put again the private key with the passphrase in the Pageant.
Do you know how to save permanently the passphrase?