[The Connection to Xbox Live has been lost.]

Ive also been getting a "connection to Xbox Live lost" issue with an open NAT and the proper ports forwarded.  I was able to fix the issue tonight by disabling IPv6 on my router.

Prior to that I was getting kicked out around every 30-40 mins, sometimes more often.  After disabling IPv6 Ive been doing hour long survivals, 20+ wave defense missions, solos, public matchmaking, and matches with friends only.

So if you're having the same issue, give disabling IPv6 a try.  Looks like its working for me.

Hope this helps!