It remembers the position on a per video basis, if I am not mistaken. What you seem to be asking for is a global setting to positioning subtitles that will apply to all videos.
Indeed it does. I believe it also makes a best guess of where to put the Subtitles on a new video, based on aspect ratio, resolution, whether there are black bars top and bottom and so on. It sounds like the best guess doesn't suit you.
Here's what you can do:
Pick one of your movies for which you have Subtitles, and make sure they are positioned as you want. Open the tagging window for that movie and have a look at the [Playback Info] tag. It will include Subtitle position information. Copy that information. If that is the only information in the tag, the next step is easy. Just select all your movies that you wish to adjust the Subtitle position for and paste the values into the Playback tag.
Of course, if you have a bunch of movies of different aspect ratios, resolutions, etc. then the [Playback Info] tag isn't likely to be empty, and is going to show as [Varies], so you shouldn't overwrite those values. You will need to select movies in groups that have the same info in the [Playback Info] tag and paste in the additional information, or overwrite the Subtitle portion of the tag, for each group.
That was too much work, right? But that is just to fix the movies you already have. What about new movies imported?
So what you do then is edit the Auto-Import settings for Movies to apply the Subtitle info to the [Playback Info] tag during import. I'm pretty sure that will happen before any other information is applied to the [Playback Info] tag, so you won't need to worry about overwriting existing data and mucking up the video display. Of course, you may need different adjustments for different movies, but tagging on import with your preferred default value is a starting point.
Try it and see if that works for you. As always, back up your library before trying, and test on small numbers of files first.