I've looked and can't find anything in there, whilst there is nothing in the guides and documentation here. Also, searching the forums here shows people generally suggesting improvements/complaining about it, and I couldn't find anything in the market for it.

At the moment, for my site, it just seems like autosave is... gone. :/

Autosave is not gone, it leverages browser caching. If your browser is not caching correctly then it will not save the post. I personally don't have any problems with the autosave.

Same here with Autosave  no problems, Try and clear your cache from the ACP support pages

Autosave in 4.x uses browser local storage, and not the site database as it did in 3.4

If the browser has disabled the use of local storage then autosave doesn't work.

How to check if your browser has disabled the functionality.....

1) Firefox - type about:config in to the address bar and then search for dom.storage.enabled and ensure it is set to true. Also, search for dom.storage.default_quota and make sure that it isn't set to 0 (means don't allow any storage space)

2) Chrome - type chrome://settings in to the address bar and then click 'show advanced settings' and click 'content settings' under privacy. If the cookie setting is 'Block sites from setting any data' then local storage is turned off.

3) IE - go to Internet Options -> Advanced -> Security -> Enable DOM Storage. If it is not ticked, then tick it on.