It's been stated that anyone with less than more of a quarter of Saiyan heritage cannot go Super Saiyan. Some have even theorized that if someone doesn't have enough Saiyan heritage, then they will be nowhere near as powerful as the average Saiyan or even have any Saiyan-related powers.

Since there are very few full-blooded Saiyans (Goku, Vegeta...) left and most Saiyans alive are half or less (Gohan, Trunks, Pan...), after a few generations will there be no-one left who can go Super Saiyan (with the exception of the already existing and few future Saiyans with enough heritage)?

Yes, I'm aware Goku jr. is a sixteenth Saiyan and can go Super but GT isn't canon and it was probably a mistake since Toriyama has said it wouldn't be possible for anyone with that amount of heritage to go Super.

Vegeta has a little brother out there somewhere, so consider that plus other possible Saiyans.

where has this been stated ?

Akira will make sure they don't, So you don't worry about that ;)

This is a saturday morning cartoon. They could just make up a bunch of Saiyan women that survived. Boom, more super saiyans.

@kyrees: Some sort of OFFICIAL guide book written by Toriyama and he's mentioned it in other times, like interview, I think.

@evilvegeta74: But he already has some alien wife and there's no known surviving Saiyan women.

Not yet , who's to say what may happen in the future

@evilvegeta74: Personally I see 4 different possible predictions:

1. No more Saiyans except already confirmed existing ones and the few next ones to be born. The end. Full stop. Goodbye.

2. There are more survivors.

3. Even though Dragon Ball Online's canon-ness has been questioned (specially since it recently closed down), the idea that humans who are good enough can, by the right ki-manipulation and control, transform into Super Saiyans may be true to the series. But we'll have to wait for it to be introduced or confirmed.

4. I know GT isn't canon and Goku jr. shouldn't be able to go Super Saiyan, but it got me thinking that maybe Saiyan heritage could work like "muggle-born wizards" in Harry Potter. If the Saiyan/Wizard heritage is too low, they can't turn Super/Do magic. But after a few generations, the hidden Saiyan/Wizard potential could randomly resurface, resulting in Saiyan/Wizard children from almost Non-Saiyan or Muggle parents.

All of this is very possible.