Ok, so you know the lighter gets power when you hold down the cig lighter.
So the problem is the holding mechanism that holds it in until it is hot.
I guess that narrows it down to either the cig lighter is faulty or the female part is faulty.
Do you have access to another MB cig lighter (friend or something?) that you could test to see which is the problem. That would help to determine if you need a new 'female' part.
2006 E350 w/ 155k miles (Daily Driver)
1993 300E 3.2L Sedan w/ close to about 300k miles
2003 E500 Brilliant Silver (Had 217k miles when totalled!)
1989 300E with 289,000 miles (had for <1 yr while in HI)
03 CLK 500 cabrio (Mom's)
2006 C230k (Dad's)
1999 S420 (Mom's/Dad's)
2000 C230k Sport sedans
2001 CLK320 Cabrio (Mom's)
1995 C280 My First Mercedes-Benz... (155k miles. EXCEPTIONAL AUTOMOBILE. Was Very hard to let go of!)