The latest 1.9.x versions of TortoiseSVN no longer support Windows XP (1.8.12 was the last one that did). Since some of the computers I work with are stuck with XP there isn’t much sense in having it check for updates automatically.
Older versions of TortoiseSVN used to have a check box on the settings “General” page, but that apparently was removed later. Now, it is on the “Advanced” page and called “VersionCheck”. Setting it to “false” disables the check.