I usually have a sort of trial period with a new household to see if I bond with them. If I do, I may end up playing with them for a very long time. If I don't, I let their save drift to the bottom of the list. But I never delete saves. Sometimes I come back to an old unplayed save, make a new household, and let the original household be background or side characters. In fact, one of my favorite SimLit stories I'm working on started out this way.
And even the households I bonded well with and played for a very long time may eventually become less interesting to me. Often this is because whatever was their main struggle in life has become resolved and I don't have another thought on where the story should go next. Or sometimes it's because I made a decision I regret and the story took a turn that isn't working for me. Sometimes I actually just backtrack and say, "that didn't happen", set things back how they were, and have a do-over where I make a different decision and continue on from there.
@Heathertibb There's nothing wrong with starting lots of different households and only playing them for a short time if you enjoy doing that. But since you sound like you're not totally happy playing that way, you might give some thought as to what it is that causes you to lose interest. Did you take the story in a direction you didn't like? Has the main challenge that you enjoyed become less challenging? Do you find yourself in a rut making the same kinds of households over and over? There are lots of different reasons why it might not be working for you. Losing interest in a household may just be a sign that you want something different than what that particular household or story is offering you.