When I try to connect to my Android phone I will be prompted to enter my password. Below the password field, there is a checkbox with the option to save the password for future connection. I can check this option but it has no effect, the password will never be saved.
I have never used TigerVNC, but I see there is a vncpasswd command that comes with it.
That may yield the same results.
It tries to write the password here:
ls -lh $XDG_CONFIG_HOME/tigervnc/passwd
You would think TigerVNC would create that directory automatically, so it might be your XDG environment variables.
Do they exist?
systemctl --user show-environment | grep XDG
To my knowledge - the location mentioned
$XDG_CONFIG_HOME/tigervnc/passwd
is the location used to store the password used when remotely connecting to your desktop using a vnc server.
The password referenced in the OP - is stored in the systems keyring or using gvfs.
I took a stab, and I may have failed. But I did put that with a disclaimer. 
So they’re using TigerVNC’s vncviewer in Manjaro to a VNC server on a phone?
I see this from the man page of vncviewer.
-passwd, -PasswordFile password-file
If you are on a filesystem which gives you access to the password file
used by the server, you can specify it here to avoid typing it in. It will
usually be $XDG_CONFIG_HOME/tigervnc/passwd, or ~/.config/tigervnc/passwd
if the former is unset.
This example uses the same file, or are these the defaults?
It's late here, I would have to install it. (I'm just looking through the tigervnc*.zst.)Thoughts:
On my system the option states Keep password for reconnect.
I don’t see this as a persistent configuration option - it is only valid for the current connection.
In the context, I understand this as - keep the password so in the event the network connection breaks - attempt to reconnect using this password.
No - I think it is per design.
If you want to save the password across connections - you can use Remmina or Krdc.
I have done some investigations and have concluded that the specific vncviewer dialog is for the current connection - and is only used if the network connection break.
Using a remote connection management utility like Krdc on Plasma and Remmina on GTK you can instruct the connection manager to store the password. The password is then saved in the system’s keyring or wallet.
Wenn Sie ein Thema auf Englisch begonnen haben, fahren Sie bitte auf Englisch fort.
Ich habe einige Untersuchungen durchgeführt und bin zu dem Schluss gekommen, dass der spezifische vncviewer-Dialog für die aktuelle Verbindung bestimmt ist – und nur verwendet wird, wenn die Netzwerkverbindung unterbrochen wird.
Mithilfe eines Remote-Verbindungsverwaltungsprogramms wie Krdc auf Plasma und Remmina auf GTK können Sie den Verbindungsmanager anweisen, das Passwort zu speichern. Das Passwort wird dann im Schlüsselbund oder Wallet des Systems gespeichert.
KDE Plasma
pamac install krdc libvncserver
Ich habe eine Zeit lang Gnome-Connections benutzt, aber das ist hie und da eingefroren aber TigerVnc scheint das auch zu machen. Auf dem Telefon ist Droid-VNC installiert. Ich muss da noch mehr Erfahrungen sammeln, zwei Wochen reichen nicht.
I’ve been using gnome connections for a while, but that’s frozen here and there, but TigerVnc seems to be doing that too. Droid-VNC is installed on the phone. I have to gain more experience, two weeks is not enough.
Mod edit:- Translated to English for you. No charge. Please use a specific language category to post in any other language than English.
Please translate that to English.
This is the international (and thus English-spoken) part of the forum. If you wish to speak German, then kindly use the Other Languages > Deutsch category.