First off, live updating is immediate rather than "timed". Other than that though, there are a couple things you can do to get close to what I think you are trying to do but it can't be exact. It will require multiple smart playlists for set up and a "playing" playlist that references the others, and it won't be perfect.
Because the updating is immediate, the "playing" playlist will change after a song is played. This isn't as bad as it sounds, what you want to accomplish is getting the song to come up again until you "love" it - and let it hang around for a little while.
(All playlists below should live update.)
Playlist1: love = none songs.
Playlist2: Playlist1 AND not played in the last week AND plays < 15 AND limit to 4, random
Playlist3: 21 most recently played
Note that Playlist3 looks mutually exclusive from Playlist2 because if you played a song in the last week it can't be in Playlist2. You could put most of the Playlist2 criteria in Playlist1, but the main thing is that Playlist2 should be a subset of Playlist1.
PlaylistA: (any songs from) Playlist3 + Playlist2, limit to 24 least recently played. This is the playlist you actually play - play it in sequence of arrival rather than any other sequence. I chose the sizes of Playlist2 and Playlist3 for the sake of repetition which I will explain later.
Playlist3 + Playlist2 = 25 songs, but you are limiting it to 24. Because it is 24 least recently played, as soon as SongA is finished playing it will drop off PlaylistA - if it was a song from Playlist2 it will jump into Playlist3, the least recently played song from Playlist3 will vanish from the list, and Song$ will be added to Playlist2 AND SongZ will be added to the end of PlaylistA. After SongB on PlaylistA finishes playing, it will drop off PlaylistA - if it was on Playlist3 already it will move to the end of it and either SongA or Song$ will be added to the end of PlaylistA, depending on the randomization engine.
Once a song drops off Playlist3, it can only return to Playlist2 in a week or more IF you didn't "love" it AND it hasn't played 15 times. The songs dropping off Playlist2 and Playlist3 happen immediately, not every week. You might want to experiment to see how long it takes for a song to fall off Playlist3 - the randomization engine may make some songs stick around for a a long time before it gets victimized while a song from Playlist2 may only rotate through Playlist3 a couple times before it falls off Playlist3. I guessed that a proportion of 4:21 would keep a song rotating for about a week - at an average of 4 minutes per song you will get a "new" unloved song every 20 minutes or so until you've exhausted Playlist1 or Playlist2. So you'll "lose" a song from Playlist3 every 90 minutes or so - if my math is right (and it probably isn't) a song may rotate about 10 times through before it falls off Playlist3. If you "love" a song that is in Playlist2, it will drop immediately and NOT go to playlist3 since you didn't let it finish playing so you might need to be cognizant of what you are "loving".