The way it currently works - at least, the way I designed it, and the way it seems to work for me - is that it doesn't remember anything between visits, but rather determines which comments are new since your last visit by looking at the highlight provided by LW's server. If there were comments made since your last visit, they should be highlighted with or without the script; no custom highlighting will be performed until you manually change the timestamp.

If you aren't seeing new comments highlighted, it's (almost certainly) because LW isn't highlighting them - maybe you're logged out, or loaded the page elsewhere, or have never visited the page? [In this way the LW script differs from the SSC script, because the LW server regards "never visited" as "nothing new" whereas my SSC script regards "never visited" as "everything new".]

The reason I did it this way is that LW, unlike SSC, is itself keeping a record of which comments are new since your last visit, which works even if you loaded the page on another computer (but the same account). I didn't want to mess with the built-in mechanism, only allow you to change it per-visit if necessary.