This cyclic ON-OFF operation of the joule thief happens near the end of the battery life.
In above case the voltage drops down to below 0.4 Volts. I have had some even go as low as 0.35 Volts with a single LED.
This Joule thief has been running for one week with a "flat" battery starting at 1.1 Volts. It is still running in the ON-OFF cycle for the last 24 hours.
The coil is not critical and is bifilar 14 turns on a small toroid, driving via a BC 549 two green LED's in series. a 1 k.ohm resistor is connected in the base.