"Cut-outs" usually come from bad connections. It would be worth trying a fresh set of plugs on the Battery, and the ESC. Many times, "Fake plugs" cause this problem or battery packs that have adapters or "universal" style plugs on them.
Could be the battery "sapping out". Happens often.
You can test by "Turning off" the lipo protection to see if it helps at all and runs longer than 30 seconds.
What you're experiencing sounds to us like "False Lipo" protection. It seems, the ESC "Thinks" the battery is dead when it's not. So for that 30 seconds, voltage is dipping down, and tricking the ESC. When it stops and sits, the voltage rises back up, and the ESC thinks it's okay to go again. So it does, then the same thing happens. This is a common situation that happens to many hobby folks, usually related to a battery, connector, or basic solder/wiring problem long before it's anything "Wrong with the ESC" so to speak.
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