Postico never finishes connecting to a database

Connecting to our 'production' database never completes - we see "Connecting…" in the status bar, a spinner at the bottom right, but only "SQL Query" in the main window display. Connecting to different databases on the same server works pretty much instantly (including databases that are older clones of the non-responding database). We can successfully connect to the non-responding database using PgAdminIII so it looks to be Postico-related.

We'd be happy to provide logging info if available...?

No source files or tests are identified. Start by reproducing the connection hang with the production database and comparing it with the working clones and PgAdminIII; use the project's available logging to isolate the connection stage, with the issue done when the affected database connects normally in Postico.

Written by the indexing model from the issue text.