This has recently started to happen here, too, and hadn't before.
I use Firefox, cookies managed (and whitelisted) with Ccleaner.
Only recent change is a Fx add-on installed called
Better Privacy (which deletes "super" or flash-based cookies on exit.)
Has Pprune recently taken to using flash-based cookies? Nothing else I've thought of explains this.
Once logged in, the site works normally.