Another thread here explain this problem with the GPS and IRIDIUM unit Garmin 700i and probably also the 750i. They turn themselves off randomly if on for a long time. I have been testing a lot. Cradle or no cradle, 12V power or USB power. External antenna or not. Nothing of this solved my problem. I replaced my first unit, then same problem with the second one.
I found that if it was inside a building or my boat with no satellite coverage it did not turn itself off. Then I tried with the unit inside but with an external antenna outside. It stayed on. Then I removed the internal antenna totally, mounted it in my cradle with 12V power and an external antenna. It did not turn itself off in one week. Today I mounted the internal antenna back. It turned itself off after 2 hrs.
Garmin - we need a replacement internal antenna or a FW upgrade. This is most likely because of both GPS and IRIDIUM in the same small antenna. Interference.