Hi,
It does not need resetting, there are no static things that should change the outcome.
Multisites are a bit weird to handle, but can so try switching to the current site back after every ASP_Query loop, like this:
restore_current_blog();
I have checked the queries, but I don’t see a missing switch anywhere. This is very likely the cause though, as to search across the sites a switch_to_blog() is called, and after it’s finished the plugin reverts back to the current via restore_current_blog();
My guess is that there is either a missing restore_current_blog(); somewhere I didn’t notice, or it does not have an effect.