What we got is a small Batterypowered Table Lamp:

"Philips LED Tischleuchte, batteriebetrieben, tragbar, weiß [Energieklasse A+]"

• High quality LED light
• On / off switch on the product
  
• Automatic switch off after 15 minutes (Unwanted Feature!)
  
• Lightweight and portable for total flexibility Battery operated - No cables or power outlet required (3x AA included)
  
• Scope of supply: Philips Moodlighting LED table lamp, white

From first view a lovely table lamp. But it is also very annoying, that it shuts down after only 15 Minutes.

I checked all components on the PCB:

• U1 MJX0084 or less likely MJXOO84 - it was long ago that i got that less results on google
• Q1 "2306" most probably: https://de.farnell.com/taiwan-semiconductor/tsm2306cx/mosfet-n-kanal-30v-3-5a-sot23/dp/1864577
  
  • Drain: Connected to Battery -
  • Source: Connected to LED-
  • Gate: Connected to Pin 6 of U1 via R2 (1k)
• Push Button on PCB (THT)
  • Connects Pin 2 of U1 to Battery - if pressed
    R1 1k Most probably 0805 SMD
    C1 Maybe 100nF?
• Battery (via cable): 3x AA Cell (4.8V) http://www.goldenpower.com/eco/en/product/carbon
  • MODEL NUMBER    GR6M
  • NOMINAL VOLTAGE (V) 1.5
  • DIMENSIONS (mm)    
  • Diameter: 14.0
  • Height: 50.0
  • AVERAGE WEIGHT (g)     16.5
  • CROSS REFERENCE    IEC: R6P    ANSI: 15D     JIS: R6P
  • Since it might be a zinc–carbon (dry cell) .. AA batteries have around 400–900 milliampere hours capacity So assume 800mAh per Cell.

• LED(s) (via cable)
  • Current ~ 102mA
  • Voltage: ~ 4,8V
  • Power: < 0,5W (Claims 0,57W)
  • Apearance: Warmwhite

So the U1 is a "black box" there is AFAIK not much to do with the existing pcb.

The "Sleep Current" is about < 0,2µA @ 4,8V.

So there are some possible solutions:

• Using of a physical On/Off Switch
  • Pro: Really Easy
  • Pro: Idle Power Consumption: ~0µA
  • Con: Hard to gain a WAF > 1.
  • Con: Outer Mechanics need to be Modified
  • Con: Low Nerd Cred
• Using a CMOS circuit which toggles between On and Off
  • Pro: May be easy to store it inside the lamp socket
  • Pro: Its no black magic
  • Con: Medium Nerd Cred
  • Con: Power Consumption of > 8µA *.
• Using a MSP430
  • Pro: High Nerd Cred
  • Pro: Easy programmable Features (Can be adjusted later easily..)
  • Pro: Can be made to turn on/off every Day
  • Pro: Can be Made to turn off after a programmed time
  • Pro: Can be extended to a general purpose pcb
  • Pro: The LED could be PWM dimmed
  • Con: Power Consumption in Power Save: ~8,5µA - 85µA* depending on Voltage
  • Con: Needs a 3.3V Voltage Regulator

* Maybe there would be a possibility to enable the Power only after press of the Button?.. if not it would definitely break the energy rating (Battery Life).

I'm still open for further Ideas. Please let me know in the comments.