I can't find any specific timeframe for the first 4 stay bonuses. So far, we've stayed twice, and both bonuses have posted (although for one stay I did have to fax in the folio - it hadn't posted automatically despite all the information being present on the record). Both stays were within the first 60 days I had the card, if that helps.
The one bonus that did not post was for the additional cardholder. I had requested that card with my initial application, but the bonus never showed up. A telephone call to HHonors customer service resulted in an immediate 2500 point Service Adjustment to cover the missing bonus. I was impressed by the responsiveness of the customer service representative.
My thanks to the OP of this offer!