Solution 1:

If you update your browser, you might want to rollback the update or to undo it.
Mostly used in database management, I often hear/read about rollback of driver updates or program installs.

Solution 2:

It depends.

  • If you just don't update stuff, you let it become obsolete/old/out-of-date, let it age, olden, or dust. A stronger and more colloquial expression would be, you let it rot. However, the most straightforward thing to say would be, you just don't update it.
  • If you actively perform the opposite of updating, you make it old or revert it to an older state. A more eccentric word would be, you antique it.