I had a similar problem with our '89 300E, only it was intermitent. I busted my tail trying to figure it out for almost two years. Basically, it boiled down to two problems.
The alternator wasn't putting out enough voltage, and therefore there wasn't enough juice in the battery to keep the ABS going. The alternator problem was due to an oil leak on the front of the motor. It's called "oil soak", and the oil residue builds up on the armature of the alternator, preventing completion of the current ultimately to the battery. In addition to all of this, the voltage protector to the ABS's brain wasn't working consistently.
In the process of discovering all this, I found out something about the sensors everyone is talking about. They're basically nothing more than tiny electricity generators. They have an internal magnetic plunger that is spring loaded. Every time a tooth on the gear on the wheel passes the tip of the plunger, it causes the plunger to move within the housing. When the tooth passes, the spring pushes the plunger back. This back and forth motion causes electricity to be generated. This is what the ABS brain reads.
I removed my sensors from the car, and hooked up a multimeter to them. I then, in quick succession, moved a steel knive against the end of the sensor repeatedly, watching the multimeters readings. Of course they weren't consistent due to the crude method of my testing, but I did get spikes when voltage was being generated.
Never the less, I let an independent tech convince me that the sensors were bad. Stupid move on my part, as $400 later the problem still wasn't fixed.
So I finally took it to the delership and let them hook up their magic box to test everything. And they are the ones who told me about the voltage protector problem.
Now, since they fixed that and I took care of the alternator, I no longer have a problem.
The moral to this lengthy story, IMHO, is to pay the dealer their $90 for an hours worth of diagnostics time and then fix the problem yourself if you're so inclined.