From the Super Mario Wiki, the Mario encyclopedia
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The Flip Meter (also called Flip Gauge) is a meter in Super Paper Mario and Paper Mario: Color Splash. When Mario uses his Flip move, it will start decreasing every two seconds in Super Paper Mario or every second in Paper Mario: Color Splash.
Super Paper Mario
In Super Paper Mario, when the meter is empty, Mario will lose one HP, and the meter will immediately refill. If Mario flips to 2-D, then the meter will slowly start getting the points it lost back, but it does not need to be full for Mario to flip to 3-D. The Flip Meter only appears in 3-D or when it is getting its points back.
If the heroes collect the Mario Catch Card in the Flopside Pit of 100 Trials, the Flip Meter will never decrease, enabling Mario to stay in 3-D for an unlimited amount of time. If the player decides not to take on the Flopside Pit of 100 Trials, they can use a Long-Last Shake or another item that causes HP restoration to prevent the Flip Meter from emptying.
Paper Mario: Color Splash
In Paper Mario: Color Splash, the meter has an appearance similar to the timer featured in Super Mario Bros. 3 and starts at 10 units. It does not show up when in 2-D mode, as well. When it's empty, however, Mario does not lose any HP, but is instead forced to return to the 2-D perspective. Furthermore, it is completely filled as soon as Mario returns to said perspective.