Yes, that’s what that kind of searching does. Unfortunately, there’s nothing much that can be done about this. For Relevanssi, each individual search is independent and Relevanssi can’t know which one’s the last one. Logging and live search is not a great combination.
One solution I’ve been thinking about is disabling logging when Relevanssi Live Ajax Search is used and then having Relevanssi Live Ajax Search trigger logging when the user interacts with the search – but that, of course, would only work with Relevanssi Live Ajax Search, and it would mean the unsuccessful searches are not logged at all, so that’s not a perfect solution either.
If you’re seeing lots of these kinds of searches, one thing that may help is adjusting the search delay in the live search plugin, if that’s possible. If there’s a longer delay between typing and triggering the search, you’d see fewer of these intermediate searches. That would save server resources.