I'm not familiar with your motor, but how many amps will it draw at WOT with that prop?

You really don't need to "baby" your Phoenix 10 ESC. It protects itself and the battery in these ways:

1) Your low voltage cutoff. As Flypaper said, and if he's right in that your flight interruption comes about because your LCV is tripping, a higher current battery would stop this. Personally, I'd never do this as I always want a battery that has 5 to 10 minutes of flight time an NO MORE. That's my threshold for pain on carrying around extra weight, but you may appreciate the extra time and power. I usually program my LVC to 5V, so it will NEVER trip with either a 2 or 3 cell pack. I rely on detecting a low battery voltage when hovering power gets noticeably lower.

2) The current limit feature of the PH 10 may be set to a hard cutoff. Reprogram it for a soft one.

3) Your Phoenix 10 will shut off if it overtemps. Of course, this is not a good thing, but the miracle is it will just simply reset when it cools off. (the plane will cut power, but you'll hear it "beep beep beep" when it cools off and it's immediately ready to fly again (assuming you don't wreck your fragile tensor). I moved my ESC into the airstream and fixed this problem in my own applicatin which was drawing 10-13A at WOT.

The president of our local electric flying club told me that the 10A rating on the ESC is conservative, and the chips are actually rated for 15A. From my own experiments, I beleive this, and I have yet to ruin a Phoenix 10, or a battery from programming it as described.