Every time if flash the firmware it is from the same file in the same folder. Why does the plugin forget it?
OctoPrint-FirmwareUpdater is a plugin so this question might best be asked in an issue on its homepage.
Yes but some devs don't like github issues for support questions, which is why I tried the forum first.
Is there a reason why the filename isn't saved like the rest of the parameters?
I can actually save it but when it is used to flash the file it disappears.
I suppose it is a bit different from other saved parameters because it refers to a file on the web client, not the server. So if I viewed the settings from another machine it would not be relevant. I.e. it would need to be saved in a client specific place such as a cookie.
The firmware update is a bit odd anyway in that it runs from the settings dialog. I expected it to add a new menu option.
All of your questions are good ones but the author of the plugin is the best source of answers. If they don't frequent these forums, then an issue on the plugin's homepage may be the best contact method.
You might try the Marlin Flasher plugin instead.