There is a limit of 12 plays per person.  I'm thinking maybe some of us have hit this limit?

Have you read the Rules for this one?  I think they're sort of confusing.  From what I gather, the overall contest runs for several months, but there are different game periods within that time.  Perhaps we're in the lull between entry periods?  Again, I can't claim to be an expert on this one.  Lots of people had trouble even running this game and I don't think it's very well explained.  How that we're on their mailing list, hopefully they'll send a notice when we can start entering again.

The Instant Win game was only for a few days:
The Instant Win Game begins at 12:00 a.m. Eastern Time ("ET"), August 28, 2006 and ends at 11:59 p.m. ET, September 1, 2006 (the "Promotion Period").

The Sweepstakes entry is:
The Sweepstakes begins on July 1, 2006, at 12:00 a.m. Eastern Time ("ET") and ends on June 30, 2007, at 11:59 p.m. ET (the "Promotion Period").
*How to Enter: You are automatically entered in the Sweepstakes if you have subscribed (“opt-in”) and are currently “opted-in” for JCPenney Email Updates for promotional offers, products, and events. You will automatically receive one (1) entry into the Sweepstakes. For each month you remain opted in, you will receive another entry into the Sweepstakes; your monthly entry will be considered on the first day of the calendar month following the month for which you were opted in.
Also:
Limit: Twelve (12) Sweepstakes entries per person, limited to one “opt-in” Email address (if applicable) by any method or combination of methods of entry during the Promotion Period.

So the instant win is over but the sweepstakes is on-going until 6/30/07 & you are automatically entered if you didn't opted-out of the JCPenney emails.