Something is getting "hot" temperature wise that is causing the computer to shut the starting down.

Perhaps you car has the system that shows trouble codes. What codes are showing up (DTC's)?

When I had this problem, I found that the CPS (the one at the flywheel just below the oil filter tube) was loose. I cleaned it, tightened it down, and solved the problem. Remove it, clean it thoroughly, it's just a magnetic sensor, and re-install. If you need to replace it, replace it with a genuine German part. Yes, it's more expensive than the off-brand names from China, but they really work and work for a real long time. This is one of those parts that will strand you. It's worth the extra money to not have it happen to you. Because I changed mine as an abundance of caution, I keep the spare in the car with all my other "anti-standed emergency spare parts".

__________________
03 CLK430 Cabrio 211K Pweter Silver/ Oyster Leather
90 300SEL 214k Pearl Black/ Alto Grey/Black Leather

Prior: 85 190E, 88 300TE, 89 300TE, 90 300E 2.6, 90 300TE, 92 300E 2.6, 91 and 93 300SL, 87 Ferrari Mondial Cabrio