[MtDon]

You didn't mention who your opponent(s) would be. If you played against a finite number of opponents, who each had a finite number of chips, then it is possible for you to win, because someone would have to win all the chips.

If you play against either a finite number of players who have an infinite number of chips, or a potentially infinite number of players with a finite (or infinite) number of chips each, then you will eventually lose all your chips. This is, of course unless all the players are so bad they always throw there hands away whatever they have and what ever the board cards are - but this doesn't fit the predicate that you have a 3bb/100 advantage in the game.

Eventually, you will run in to a run of cards where you are blinded off, if you don't lose all your money before that.

If you play for an infinite lenght of time, all possible finite runs of cards will be dealt an infinite number of times. Since you will always have an finite number of chips, you will have to run into a run of cards which will break you.

For example: You will run into these cards for as long a stretch as needed. You have AsAc, the BB has KsKc. Everyone else has nothing and folds pre flop.

Flop: AdKd2h
Turn: 2d
River: Kh

Your full house will lose to his quads every time. These same cards will be repeated, consecutively or in any order needed, as many time as are necessary for you to lose all your chips.

Having an edge, doesn't protect you from a bad run of cards.

The only type of edge that would protect you from a bad run of cards is one that was due to all your opponents playing so badly that, for example, they would fold every time you bet or raised, so that you could win every hand by betting or raising. That is, they play so badly that there would be a stategy that would allow you to win every hand you played.