Take a look at this:

Celebrity Play

During each episode of the Program a Celebrity guest will appear in the final segment of the Program and will attempt to correctly answer one (1) question with a value of Fifty Thousand Dollars ($50,000). The Game Clock will be set at Forty Five (45) seconds. The Celebrity can select one (1) of the four (4) lifelines to assist him/her in answering the question. All other rules of game play apply. If the Celebrity answers the question correctly they will receive Fifty Thousand dollars ($50,000) for the charity of their choice. If the Celebrity incorrectly answers the question he/she will receiver Twenty-Five Thousand Dollars ($25,000) for the charity of their choice.

Here is a official link:

http://abc.go.com/primetime/millionaire/index?pn=rules

I wonder why we don't see the clock?

Now that's odd. There was definitely no kind of time limit imposed on the two celebrities I saw at my tapings. I think Regis even mentioned several times that he/she could take their time.

The clock is set at 45 seconds and stays at 45 seconds the entire time the STAR! is in the Hot Seat.
It never ticks down. Set it at 5 seconds if you want to. It never ticks down.
When's Lauren Conrad going to be on again?

Ok . So then what's the point of having the clock if there not using it?

There's also this:

Rules didn't say anything about it ticking down.

Nice little loophole they got.