I like the suggestion above of training with a heavier helmet. I think weighted shrug exercises along with pilates/yoga help in strengthening the core and neck muscles. The exact muscles to be strengthened are your sternocleidomastoids (SCM). I don't believe there is any exercise regime that has been created to tackle this condition. A sports physician might have better ideas.
During PBP 2015, I came down with Shermer's Neck around the 1,000 Km mark. I didn't have a neck brace and the few available at checkpoints were already gone. I just had to suck it up and ride the next 230 Km (mostly at night) to the finish line with my head drooping and mainly relying on my peripheral vision. I had left some wiggle room in my fork tube, so I was able to raise my handlebar by about one inch which helped a lot. I remember the last 80 Km or so seemed like an eternity. Luckily, Shermer's Neck doesn't hurt. Your SCM’s simply lose all strength to keep your head straight. The position used for road cycling (even striving for good form) is not a natural position for the human body and there is a limit to how long it can be sustained which varies from person to person.
It took me about a couple of days to recover about 80% of my neck strength without a neck brace and two more days to feel 100%. I have read that some people need to wear a neck brace for weeks to fully recover.
In spite of this physical grievance, I finished PBP before the 90-hour time limit.
