I ran into this problem and found nothing via search so I'm sharing the "fix".
If you pin putty portable to the start menu on windows 10, then use the "recent sessions" or "pinned sessions" that can cause this error if the saved session doesn't exist in the registry.
I originally thought it was a conflict when you have the non-portable version installed on your PC, but that's not correct. I uninstalled my local version and it had no impact.
What I did was:
* Have the non-portable version installed on my PC.
* Have "website1name" as a saved session.
* Imported my settings to putty portable https://portableapps.com/node/60898
* Was using "pinned sessions" via the windows 10 start menu.
* Changed the name of my saved session to "website1newname"
This results in the "PuTTYPortable\Data\settings" directory having the new name, and the "HKEY_CURRENT_USER\SOFTWARE\SimonTatham\PuTTY\Sessions" keeping the old name. This causes the error.
If I launch with "website1name" instead of "website1newname", or if I manually open putty-portable (not just the shortcut) and then load the session, then it works.
An "easy fix" is to run the putty.reg file at "PuTTYPortable\Data\settings", which will overwrite (or add to) the settings (in the registry) of your installed version. There may be some cases where this isn't desirable though (IE: using someone else's computer). I'm not sure if anything can be changed to make it work.