If a query is taking longer than the defined 180 seconds to run, the user should be presented with a message saying the query has timed out and will continue to run in the background.
The problem in the PCORI Web Clients (SHRINE and PHS) is the timeout message is not displaying to the user. The client will continue to display "Running" in the Query Status panel and the timer will continue to advance.
The only way to "free up" the client is to log out and log back in. Provided the query has finished running in the background, the user can drag the query from Previous Queries to the Query Tool to see the results of the query.
WARNING:
Whatever you do, DO NOT CANCEL the query because even if the query has finished running in the background the Query will be "cancelled" and the DELETE_FLAG will be set to Y. This means the query will not be visible to the user in the Previous Queries.