SQLite Manager (Firefox) does not do UPDATE statement on multiple rows

I'm confused on how I seem to fail at doing a simple update in SQLite. I've installed SQLite Manager in Firefox and I want to update the moz_places table there because we recently changed 'provider' and instead of clearing my whole history in Firefox I thought it would be nice if I could simply update the information so the history points to the new location.

The idea is to run this code:

UPDATE moz_places SET url = REPLACE(url, '.old.com/', '.new.com/')

When I press [Run SQL] I've got the impression that nothing happens even though the Last Error field shows 'not an error'. Maybe it's simply very fast? Nope, when I then go into the data I find that it did not update a thing and my places folder is still full with old.com urls.

However, when I try

UPDATE moz_places SET url = REPLACE(url, '.old.com/', '.new.com/') WHERE id = 2458

it DOES update this one record.

Naively assuming that the SQLite syntax requires a WHERE I then added

UPDATE moz_places SET url = REPLACE(url, '.old.com/', '.new.com/') WHERE id > 0

but that didn't get me any results either.

Does SQLite only allow singe-row updates? Looking around on the internet I do not see such a limitation, but otherwise I'm not sure what could be the issue.

PS: I'm doing this on a copy of the /Profiles/ folder I found in %appdata%, not directly on the 'live' version. So locking should not be an issue either.