There's 3 different things usually going on with your KTTW card: Room Access, Dining, and Tickets. At check-out your room access will expire. But, your dining credits will not expire until Midnight of check-out day. And any unused tickets on your KTTW card will remain usable until 14 days from first use of those tickets. If you never used your tickets that were on the KTTW card, you could take the card home with you, then bring it back to Disney on your next visit and start using it. Some people have all their park tickets on the first KTTW card, and take home the park tickets from the second resort to save for later. It's cheaper than buying a few days for resort stay #1 and buying a few days for resort stay #2.
So on check-out day, use up those dining credits all day! If your second resort stay has dining credits, you can start using those credits, too. But you can't combine credits from first resort stay and second resort stay, for example, to eat at a 2-credit TS.