Just thought I would report back here as I have been playing my rotation game for about 2.5 sim weeks, through 13 households so far, and decided to have a look back at some of those played to see if they still had sentiments. I could only find two households which still had any, as follows:
This one from about 3 sim days ago, you can see that the green level on the sentiment has dropped:
https://dl.dropbox.com/s/ztw11wwv6c764ob/Screenshot%202020-11-22%20184337.png?dl=0
This one from about 7 sim days ago, I'm guessing this is a stronger sentiment as it is from longer ago and the level is higher than the Closer From Happy Memories one above and the green is a darker colour:
https://dl.dropbox.com/s/rosl16kisso9knk/Screenshot%202020-11-22%20184505.png?dl=0
I found no other sentiments for anyone, so they obviously do fade and then disappear whilst you are playing other households.