I'm sorry for the delayed response.
I have started to to look into this matter. But so far I have only found a bug which has most likely nothing to do with the problem you observe.
My first thought was that the user account which you have used to alter the settings of this plugin may not have the capabilty manage_links which is the current minimum capability necessary to access the settings page.
But if the user account would not have this capability then you would had problems to access the page at all - and the problem would not only show after clicking on "Save changes".
Since this problem seems not be a general problem which happens in every blog (I could not reproduce the situation in my blogs), I think that something is different in your or my blogs.
Maybe you use a plugin which I don't use. However in order to fix this problem we need to find out what this circumstance is.
The Not Found page appears usually if the URL can not be resolved. Maybe it is something which influence or limits the way the URLs get handled/resolved. Maybe a security plugin or a custom rewrite rule in the .htaccess file.
Does the content of the .htaccess like this or does it contain other entries?
Could you tell me the names of the plugins you are using?
(or could you find out whether one of them is responsible?)