We are also experiencing this with several clients.  The primary card holder will download but not the additional authorized users.  We have to manually import.  This changed about a year ago and we suddenly started seeing it happen with all QBO clients.

The work around is to manually import the missing transactions.  I agree that whenever I call support, the support team does not seem to be aware of the issue and there is no solution in site.\

This is a huge issue and has added bookkeeping time for some clients.  Now that Intuit is offering bookkeeping, I am surprised they are not interested in helping fix. 

Intuit - please make this a priority and get with AMEX to fix.