Irespective of business processes all state machine nintex workflows are stuck on first change state action. I tested with different nintex workflows in different sitecollections but same problem. It is happening only in live/prod not in uat/dev environments. We are using onpremise SharePoint 2010 and Nintex 2010.
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I would try restarting the Timer Service. See here for a bit more information: Workflows not continuing - Timer Service and Delays
Hope this helps!