Gamma-ray bursts: A supernova connection Can the gamma ray bursts connected to a new supernova 
prevent the black hole from forming?

Quoting the abstract of the linked reference "...has become clear that probably all long GRBs are associated with type-Ic supernovae resulting from massive stars that suffered substantial mass loss...". 

If enough mass is converted into radiated energy then the condition for BH formation can vanish?
Edit Add:
Due to the lack of the expected neutrinos, the IceCube Experiment puts to trash the connection of GRB and SNe.
quoting Cosmic Varience:

More recently, a consensus had grown up that GRB’s (as they are
  called) are associated with intense beams of particles created by
  newly-born supernovae. That’s a model that seems to fit most of the
  data, anyway, and it also makes a pretty good prediction for the
  production of associated neutrinos. But a new paper by the marvelous
  IceCube experiment has thrown a spanner into the works: they should
  have been able to see those neutrinos, and they don’t.

 A: It is impossible to get rid of black holes by this mechanism, because with a sufficiently large quantity of matter, one can form a horizon with no large gravitational fields at all. If this method works to prevent certain astrophysical collapse scenarios, it cannot prevent hypothetical collapse scenarios where no gravitational field becomes large at the moment of collapse.
The key point is that the mass of a black hole forming amount of material is proportional to the radius of the black hole. This means that if you have a constant density $\rho$ in a square of side-length R, even if the density is low, a black hole necessarily forms approximately when the Schwartzschild radius of the mass is greater than the side-length.
$$ {GM\over c^2} = {G\over c^2} \rho R^3 = R$$
Solving for R:
$$ R = c\sqrt{1\over G\rho}$$
for the density of water, $\rho=10^3 {\mathrm{kg}\over \mathrm{m}^3}$, the radius is about 10$^9$ km, so a light-day radius sphere of water will collapse, with no unusual x-ray phenomena, because the gravitational field is never strong before the event horizon forms.
A: Let me start with what a long gamma-ray burst (LGRB) is. The current model says that GRBs are observed when the core of a rapidly-rotating massive star collapses into a black hole (BH). Stellar material that is accreted swirls around the BH, forms an accretion disk and launches polar jets. If the jets are pointed at us, we observe a brief (in astronomical terms), bright, relativistically blue-shifted emission: a LGRB. (Long only in the sense that they are longer than "short" GRBs, which last seconds and are probably caused by something different.)
So, the first problem with saying that the formation of a GRB is that the GRBs emission requires a BH. That is, if there's no BH, there's no GRB. The answer to your question is no.
The mass loss that you describe occurs in the massive progenitor star before core collapse. So while it's true that a 60$M_\odot$ star loses its hydrogen and helium envelopes (the absence of helium or hydrogen lines in the supernova spectrum is why it's of Type Ic), at the point of core collapse there is still about 20$M_\odot$ of stuff in the star available.
Finally, this mass is not lost because it is converted into energy. Instead, it's because the radiation produced by fusion in the core exerts a force on the envelope that, where stronger than gravity, drives material off the surface. These are known as stellar winds.
A: We assume that under extreme gravitational pressure the star must collapse into a BH because there is no known physical mechanism that can get rid of the star matter too much.  
Theoretical models of GRBs, and associated SNe, are struggling against the observations (Gamma Ray Bursts: back to the blackboard by Maxim Lyutikova).  
We have for granted that the BHs are an integral part of GR. However, GR survives even if they do not exist. The link referenced in the question make me wonder: Is it the case that BHs may not exist?
My answer is yes, provided that the energy of the particles becomes radiation (EM X-rays, gamma-rays, ..) before the star collapses. $E=mc^{2}$ allows it but the SM does not. I'm optimistic and I have to me that the LHC will teach us a lot. We must be humble and pursue other routes.  
The issue of singularities in space/time is, imo, very difficult to accept philosophically and physically and I feel better with the hope that they do not exist.
The future of physics may be different than we expected.  
Mankind has the hopes placed in physics because it is a theme central to our collective future. Thankfully, the GUT is not there just around the corner and that's good for the physicists of the future. ;-)
