We have a SpaceGear48, that I have been running for approx 3 years.
I havn't found many solutions to the problem you mentioned.
As you start cutting bevels, your material thickness increases so your cutting conditions have to compensate for that(ie more power,slower feed rate.)but as the angle off attack incresses the edge thickness decresses, so the edge over heats and blows away. Sound familiar.
You can try using Nitro as an assits gas,to stop the edge oxidising but it is a bit tricky to keep the cut dross free.
Generaly you can't cut any bevels more than 45deg.
You might want to contact Mazak directly, for cutting condition. There engineers have done it all before, and at times can be quite helpful.
P.S. If you are cutting Stainless Steel, watch out for reflected laser light when bevel cutting.
Regards.