This could be caused by lots of things. The first thing I would do is replace the "over voltage protection relay" ("OVP"). It is a well known problem with the w124 and is known to cause all sorts of weird electrical/starting problems. Do a search, there is lots of info on this site about it. If I were you I would replace it before I spent money on anything else. Almost all of the original ones have failed; even if they have not failed completely, they will cause starting problems. Its a plug-and-play part (no tools required), so don't ask your mechanic to fix it for you.
Also, how is your battery? Doesn't matter if it still seems to work, if its more than 3 years old it could be very tired and not strong enough anymore to crank the engine fast enough when cold to start it on the first try. How are all the battery cables and connections? There is probably a lot of corrosion on the cables after all these years, so get some files and sand paper and clean both the negative and positive battery cables at the battery and the block. My brother has a '94 Acura that wouldn't start recently, and the problem was a battery cable that was so corroded it had broken apart!
The other thing you may consider is the fuel pressure regulator. It is also an inexpensive part. It maintains fuel pressure in the fuel system, and if it stops working properly you won't have pressure to start the car. Consequently, it might take a few times to start after the car has been sitting (sound familiar?). But that's a bit of a stretch. I'd do the OVP relay first, along with a general tune-up.
Good luck.
GregS
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