Lithium-polymer battery (1 cell-3.7V) issue

Hello,

I am using some module including Arduino pro-mini, 10-DOF IMU, ESC, BLDE motor, and servo motor.
I supply the power source, 1 cell lithium-polymer battery 3.7V, to the module.

When I fully charge the battery, multimeter shows the voltage of the battery as about 4.12~4.15V.
When my platform stops being work, multimeter shows the voltage as about 4.00~4.03V.

I know that the battery can be used until 3.7V. However, As I said, my platform stops at near the 4V.
Do I know wrong something? or my batteries have a problem?

Can you give any advice?

Thanks.

The promini will work @4V.
Schematic? parts? (info missing)

Does your ESC expect 5V logic input? Have you tested it at 3.3V?

The IMU - is it 3V-5V agnostic? (many are)