is one or both using a persistant connection but each is using different login details?
Actually thinking about it
Seems likely that each one is over writting the others classes. Say they construct the class then store the object in a session thats being over ridden? Or only establish a persistant connection on construct.
Unless you are somehow invoking WordPress from within your CI application (or vice versa), it should not matter. If either or both are using persistent connections via mysql_pconnect(), I would recommend changing them to use the regular, non-persistent mysql_connect(), as persistent connections have a tendency to eat up DB processes instead of the expected saving of processes, unless everything about your application and DB environment and configuration is just so.
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~ Terry Pratchett in Nation