Hi, my name is Ed. Welcome to JustAnswer!.
If - by cuts out - you mean that you have a momentary or repeating misfire, chances are good that it's being caused by a flashover condition at one or more spark plug-coil assemblies. Each cylinder gets its own ignition coil that's installed directly atop the spark plug, shortening the path that secondary ignition (spark) has to take. That's all good until electrical resistance needed to jump the spark plug gap exceeds that of just having the spark leak down the outside of the plug. Each time spark "flashes over" the spark plug, it will etch a little bigger track in the upper spark plug insulator and inner coil boot, making it just a little easier for the next spark to follow the same path. Flashover tracking is usually pretty load-dependent in its earlier stages, preferring to leak to ground under circumstances like you've described, but not be felt otherwise. When it gets bad enough, misfire will happen almost continuously, setting a code and turning the MIL on.
A visual inspection or replacement of the spark plug set would likely turn up the offending parties. Any black mark on the spark plug upper insulator that won't scratch off with a fingernail IS flashover tracking and there's no fix for it. You need to replace the plug and coil at the same time or the tracking left in the other part will just cause immediate failure of the new one. These engines run a very long time on a set of plugs and it becomes easy to forget that we used to replace them at 30,000 miles (as is recommended with the 4.7 still). But they'll just keep plugging along until flashover begins and that could be well over 100K miles worth of wear, which is considerable.
If you happen to have a CHECK ENGINE light illumination now, you likely have a code relevant to the problem stored and waiting to be read. Let me know.
Another situation that can better be called cutting out can be caused by a wiring abrasion that happens on the passenger side-top-rear of the engine, where a large wiring harness trunk drops down from the wiper cowl and disappears behind the cylinder head. It's right back there - where you can't see very well - that a sharp machined edge of the cylinder head can gnaw into the wiring loom, shorting selective circuits in circumstances such as yours.
To help diagnose, start the engine and pop the hood. Place a stool on the passenger side fender area.
Reach over the air cleaner duct and lightly tug forward and down on the wiring harness. If the engine exhibits ANY displeasure with what you've done, by all means do it again. Be careful to avoid over-manipulation of the wiring because it can momentarily reposition the loom, temporarily putting the problem into remission (only to return later). If you identify a wiring problem back there, the easiest fix would be to wire-tie the loom up and away from where it lies naturally to prevent shorting. Pulling the loom out physically to locate and patch the problem area would be better and this would weather-seal the loom, but it's not easy of course.
Check these couple of things out and let me know if you have any questions or problems.