How do I smooth current dips on a USB charger?
The issue appears to be the USB master going into thermal reset due to sustained high current draw. It could as well be resetting due to overcurrent protection, but that generally wouldn't kick in after 35 seconds but much sooner.

Caveat Emptor:

If the USB port simply cannot supply as much current as the device requires over a sustained period, neither of the two solutions below will do you the least bit of good. The resets will continue, at best with a longer cycle than 35 seconds, and at worst even faster because the capacitor charging trips overcurrent protection.

Simple solution: Hefty capacitor between +5V and GND lines. Start with a 4700 uF 12 Volt electrolytic (just because those are common enough, and inexpensive). If that doesn't work well enough, keep adding more. 

More complex solution: An inductor-capacitor combination: Two hefty inductors, say 100 uH 1 Ampere each (just because those are common enough, and inexpensive), on the +5V and the GND lines, followed by a capacitor between them.







simulate this circuit &ndash; Schematic created using CircuitLab

The inductors will slow down the inrush current spike when the capacitor is charging up at power on. This prevents the USB port from going into overcurrent protection / reset.