Can you put together the shortest possible set of steps to reproduce the problem? Please go into details (like, where you click, what key do you press, etc...).
Also please describe how did configure the Notepad++ in WinSCP.

Yes, that's right, the error comes from Notepad++.

I suppose the error comes from Notepad++, right?

I have used WinSCP + Notepad++ for some years now to edit files directly on the server. If get error dialog "Save failed / Please check whether if this file is opened in another program" when trying to save a second file (one file at a time works fine) and this error comes only when I'm on a WLAN connection (wifi).

Editing and saving multiple files is fine on wired Ethernet connection! I have used two different computers and different networks and the scheme is always the same: multiple file saving only works on ethernet connection, not on wifi. Any ideas on this one? I just updated the latest WinSCP 4.3.5 and tried also the 5.0.2 beta.