No. There is no limit to how much a player may win in aggregate playing in any of the games, but there is a maximum single-event, individual prize and there maybe daily or monthly prize redemption limits. Please see the Official Sweepstakes Rules for more information.
Currently, the top prize available for a single play of any game using Gold Coins is 125 million Gold Coins and the top prize available for a single play of any game using Sweeps Coins is 5,000.00 redeemable Sweeps Coins.
Also, any player may play as many games as they choose, and as often and as many times as they choose. However, to play games, players first must create an account on the Golden Hearts Games website, and then acquire Gold Coins or Sweeps Coins.