
The problem with the seedless edible bananas that we think of is that that they are unable to reproduce. All sweet banana plants are clones produced from cuttings taken from other banana plants.
In the 50's the variety available at the time was the Gros Michel and it was almost completely wiped out by panama disease. Luckily we had the current variety called the Cavendish as a stand by although it took time for it to be accepted. This modern variety is now under attack from both the panama disease and black sigotoka fungus.
We only manage to produce the amount of bananas that we do today with heavy spraying of pesticides, sometimes as many as 50 times a season. As the fungi become resistant to these the crops are being destroyed. Because of the lack of diversity in the banana plant they are unable to produce a defence on their own.
I doubt very much that the Cavendish will become extinct but it is likely that unless something changes it will be impossible to cultivate it on a large scale in the near future.
There are many other seeded varieties of bananas but these are not sweet and need to be cooked. GM may hold a key, crossing inedible varieties to produce a new sweet variety with this in mind scientists are mapping the banana genome. Of course another alternative is for us all to adjust to a different type of banana.
There will still be bananas in the future but they will probably look and taste very different.