I have the same adapter and when this happens I have to open Dolphin and press "GCPad" on the toolbar and then "Refresh". You should see the dot on the main stick go from dark grey to red so you know it's working. This is annoying because it keeps happening about every 20 minutes for me and I haven't found a fix for that yet.
If you're having the same issue as me then it seems as if it's a problem with the adapter, not dolphin.
If you're having the same issue as me then it seems as if it's a problem with the adapter, not dolphin.