I am pretty sure they do lots every so often.
But that seems to be for the bigger games that stick around longer, such as the Jumbo Bucks and Big Money Maker. I have noticed the prize amounts on these games go up after coming down.
However you will notice games that go through the entire run of actual ticket numbers (the middle number on the back of the card), then they will start a new number for that game.
For instance, the Giant Jumbo Bucks is number 245 right now, it used to be 200. They start them at 245-123456-### and go up to, I am assuming, 245-999999-###. After that they will have to start a new number (replacing the 245 with whatever they go with).
I remember the $10 Big Money Maker used to be all green, now it has a red border. But it is still game number 140 so I guess they havent sold all the way up to 999999.
As for remaining prizes being shipped out randomly, well its pretty obvious somebody 'holds' the big winners and sends them periodically.
Most games starting out have maybe 3 or 4 TOP prizes, so its not like they are going to distribute them to the whole state all at once. By holding on to them longer they garnish more sales from suckers like us who continue to seek the 'golden ticket'.
On a side note, it seems the wins are fewer than ever right now. I dont expect to win every time, or even very often, but lately the wins (even small ones) just dont seem to be out there. Maybe they are saving them for the Holidays, or maybe I'm just on a heck of a unlucky streak.
Anyway, welcome to the site and keep us updated! Good luck with your wins!