Mine did this from day one, right out of the box (May manf date). It was annoying but I lived with it as the console otherwise worked fine. Then, after a month, my 360 would freeze on occasion. Not a lot, just once here and there. After another month of this occasional freezing, it started freezing on boot-up 90% of the time. I don't know if the two problems were related, but of course I sent it in for repairs.
Three weeks later, a replacement system (Sept manf date) arrived at my door. Set it up, hit power... and nothing. Same problem. Immediately call MS to vent, got routed to a supervisor. I explained the problem and my concerns about it possibly evolving into the freezing issue again and was flat out told: "send it in again... it will only get worse." So I did.
If you've still got your warranty, I highly suggest you send it in for repairs. If not, I hope she was wrong and they are not related.
On a side note, just to finish the story... the third console I received after the above repair call did boot fine on first power on... whew! Unfortunately, I received it during the short time that the Fall Update still had the E71 glitch in it and didn't know about it. Well, you can guess the rest of the story... BACK TO MICROSOFT FOR THE THIRD TIME!
Still waiting for it to come back...