Intermittent Engine Failure
I wish I could assist on where to look. This could be an issue with your new battery. I had a similar issue one time and it was the crankshaft sensor was failing. It took over a month to find it. Since the problem is consistent, I'd bet the fault codes would pinpoint the issue(s). If you don't have access to a diagnostic tool, a visit to a dealer is what I would do.
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