That tab refreshing thing really bugs me with fan fiction. If I think I might want to reread a story someday I'll download it, because if you read fan fiction you learn that many authors come back and fiddle with their earlier stories, sometimes even replacing the entire old story with chapter 1 of a complete rewrite. Even in the rare case that they actually do eventually finish the rewrite it is often not as good as the original.
AO3 HTML downloads have the story in one long HTML file. When reading that on iPad that stupid refresh can move you to the top which is pretty damned annoying.
For that very particular situation I do have a workaround, but it involved adding some JavaScript to the download HTML. If anyone else is reading downloaded AO3 HTML and would like this I've put it on pastebin.com. Get saveplace.js [1] and ao3book.css [2] and add this at the end of the head of your AO3 download:
<script type="text/javascript" src="saveplace.js"></script>
<link rel="StyleSheet" href="ao3book.css" type="text/css"/>
Saveplace does two things.First, to address the tab refresh problem, whenever you change your position in the story it waits until you've stopped at a new position for a bit and then records the new position in parameters on the URL. After a refresh happens it looks for those parameters and restores the last saved position.
Second, to make the story easier to read it hides all but the first chapter, adds buttons to move forward and back by chapter, and adds a dropdown to select chapters. It also adds a button to switch between night and day mode. The day/night mode setting is saved in local storage.
Feel free to use this in anything of your own. The chapter navigation stuff is tied to AO3's HTML, but that would be easy to delete leaving just the position saving/restoring. This is in the public domain in places where it is possible to put things in the public domain. If one of us is somewhere that isn't possible you can use it under the MIT No Attribution license (MIT-0).
Calibre can convert HTML to ePub, which you can then use reader apps for. Those are much better at remembering your place.