When i google it i find a post somewhere saying about increase the number of threads and the number of the pool, but nothing about this limitation! :( What kind of limitation? Instead of raising number of threads on one zope instance you should just use few Zope instances with smaller number of threads. AFAIK it's more effective.
I will test DeadlockDebugger, but the main problem is only happen in the morning (around 8:00am-10:00am. So install deadlockdebugger and look at it's output between 8:00-10:00. It may be safely used on production instances.
Also check if some external resources like LDAP are not restarted/backed up or sth. like that at this time, or before (eg. there is a backup at night that causes 'something' wrong for connections from your zope and your users start working since 8:00 - thats when you see 'hangup'). -- Maciej Wisniowski