I'm actually glad that this happened to you! I didn't want to answer your original post because I was starting to see you move into a very bad pattern (stimulus addiction) and I KNOW for a fact that a stimulus addict will NOT listen to advice... he has to suffer the ill effects to understand.
Now, are two-a-days beneficial? Yes, if you can recover from them. Now... recovering from them is a matter of several things:
1) Body's tolerance to training... this is normally developed by GRADUALLY increasing frequency. Elite athletes do not start out at 2 daily session... they might train 4 days a week for a few years, then 5 days a week, 6 days a week, then 6 days a week + 1 two-a-day, then 6 + 2 two-a-day, etc. It is built up over YEARS
2) Nervous system resiliency.... just like some people are more prone to burning out or suffering a depression, some people are more prone to neural fatigue and/or adrenal burnout
3) Anabolic drug use... obviously an athlete who uses drugs recover faster and can train more often
4) Nutritional status... doing frequent two-a-day while losing fat (either voluntarily by cutting calories or simply by not eating enough for your activity level) is one of the worst thing you can do for performance, looks and well-being.
5) Level of the workouts... two-a-days are normally very bad for stimulus addicts because they cannot properly modulate the amount of work or the intensity they put into each session and end up doing WAY too much or either or both.
From my experience two-a-days is best suited for performance increase (sport) or gaining muscle... and both requires an ample amount of food... if you are losing fat during two-a-days you are not consuming enough food to be able to sustain, and thrive on such a training pattern. Sure you can argue that you train twice-a-day to burn more fat/calories. To me that is a mistake because it means that the body will not have enough nutrients to recover. See, losing fat from 1 training a day is not the same thing because your body is likely to still have the ressources to recover, at least enough to avoid a crash.