I had an (extremely minor) identity crisis when I clicked on my username and saw a different identicon than I'd had previously. :)
According to this answer, your identicon is based on a hash of your last known IP address.
Since a user's profile picture part of their identity, I would prefer if my profile picture only changed through deliberate action on my part.
Since the user's IP hash is already saved (the identicon has to be displayed to people even during the unthinkable periods when we're not actively browsing), I propose preserving the first one assigned to a user, and not updating it even if the user's IP address changes.
Are there any upsides to the current behavior that I haven't thought of?