I had a similar problem when I was in Missoula, MT this summer. I had replaced the solenoid on the firewall in an attempt to resolve the issue about 3 weeks earlier, it turns out it was the solenoid on the starter. The solenoid on the starter could be changed, however we elected to change the entire assembly including the on starter solenoid. As it was explained to me the new model has an upgraded model that has a larger input voltage. It is made by Delco Remy and available from Freightliner (see attached photo).
this may NOT be the correct part # for your engine, check with Cummins.
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