Is it possible that the thing has an internal overheat sensor, and after running for an extended period, it shuts itself down? If so, it should be described in the manual.
If the water gets extremely hot, it sounds like you do not have a tempering valve installed on the outlet, or if you do, it is malfunctioning. From what I've read, this is a requirement. You may want to check that.
It's also possible that after you've used up all the water in the bladder tank (that's had a chance to warm up from the deep well water's temp), the now much colder water directly from the well means the tankless just can't raise the water to the same temperature. Say the water in the tank warms up to room temp, that's around 70 and the water from the well is say 50, the tankless can only raise the temp so many degrees as it passes by and now it's starting out 20-degrees colder.