Prior to my retirement from my professorial gig at the medical school this past December, I taught muscle physiology in the first year medical student curriculum. We are at the mercy to the laws of physiology of muscle fiber development. So it takes about 2-6 weeks for muscle to adapt to new stress without damaging fibers. At the end of that 2-6 week span, one can add another 20% duration to the work out. So if 45 minutes is all you can do at this point, continue for several weeks at 45 minutes, than in that new week add 45 x 0.20 or about 10 minutes to the next week (55 minutes) and stay with that for another several weeks. Then advance another 20%. Keep doing this at these intervals until you reach your goal.
Let fatigue be your friend. When you loose control or start leaking air, step away from the horn for the day and start back at it tomorrow.
Let me know how this works out.