Maybe a feature for key password storage can be added in the future :), even if it can pose a security risk.
Pageant is a solution, but it require to enter the key password at each reboot.
The problem is now solved by using a private key without password.
Yesterday I've updated my old Winscp (5.5.1) to the latest stable version (5.9.6-Portable) deleting old ini file and creating new connection profiles from scratch.
The problem I noticed is that while with the previous version the private key password was stored and never asked when connecting to a server, now I have to enter the key password each time I establish a connection.
If I uncheck "Tools > Preferences > Security > Session password > Remember password for duration of session" option, an option to remember the key password is shown when connecting, but it's ignored each time I connect again.
Any suggestion for this issue is welcomed.