Even without the 3001 error lockouts, we are having multiple error messages popping up trying to log into the game or selecting/logging out of a character. The problem is so bad that another member of my family keeps getting booted off the game by the error messages, and she is using another computer and account (but same router). And all these errors started popping up on June 3. Each of these errors causes a long wait and getting kicked back to a prior page or entry point. The errors are:

FFXI-3001
FFXI-3100
POL-0011
POL-1160
"Search Failed" while using the AH
"Lines Congested" while using Delivery Service

The one thing all these error messages have in common is:
"Server is busy or no response from server"

I have not experimented much without the router, but I think these errors (except for the 3001) still pop up without the router. Others in the house are using the router now, so I will check that out at a later time.

I hope that I will not have to do what the guy on page 3 said (his LS buddies solved their 3001 problems by buying a new router). Unless SE can fix the bug (if it is one on their end), I may have to do that. The router is only 2 months old.