If hosted on a WebDAV-enabled server, TiddlyWiki will automatically save changes via HTTP.
Many NAS or Subversion servers support WebDAV out of the box. Setting up your own server might take some effort though:
dav-server is a quick way to serve up a folder of HTML TiddlyWikis.
webdav server for Android lets you put wikis in your pocket. You can share with other devices on the local network too.
WebDAV support was added Feb 16 2016. If you created your wiki before that, you'll need to Upgrade to enable WebDAV.
Mario Pietsch has created several videos that show how to prepare Microsoft Internet Information Service (IIS) to host a local TiddlyWiki using WebDav
Several WebDAV hosting services tested (box.com, swissdisk.com) don't support accessing HTML files via a webbrowser, so they won't work with TiddlyWiki. However, The GMX mediacenter (www.gmx.net) has been reported as working with WebDAV with a free account.