Car turns off while driving and won't start back up

We have a F-250 we use to pull a horse trailer. When we haul, it has been shutting off while driving, about a mile or two out on regular street roads. It has not shut off on the freeway.

Typically, once it shuts off it won't start again for about 10-30 minutes. Sometime it will turn the starter and just not start. Other times, it tries one turn of the starter and stops like the starter won't work. We have noticed that the coolant appears empty and will fill it while waiting. A couple months ago, the coolant leaked out while parked and we couldn't figure out why or where. I don't know if this could be related. Sometimes if we allow the truck to roll, it will start after that. Also we recently replaced the battery, but this still happens.

We have taken this into two mechanics who can't replicate the issue and said they couldn't tell what was wrong. Not sure what to do at this point. Any ideas as to what might be going on?