The important thing to note here is that once a positive balance reports, your points will come back.
As @jcooks learned, the lesson is to use the fact that Chase reports zero to your advantage. Maintain a positive balance on a card from another bank, and zero out your Chase card when it reports a positive balance you'd like to eliminate.
That said, Chase will report your current balance at any time you ask them to. If all your cards are at zero, you can bring your Chase card to your desired balance and call in. The new balance will show up on your reports in a couple of days.
I wouldn't overuse this service, though. Use it when there's a real benefit, such as a time when all your card balances are at zero and you're applying for important credit. I used it when I had a myFICO report that was about to expire and my balance situation was almost identical to my previous pull.
