I had an identical issue to yours this past winter. Even went as far as to remove outside cover and leave off - no issue. When cover reinstalled unit would run for about 15 - 30 minutes and shut off.
Found issue was thermal switch(it is usually a black round "button" mounted on heat box with 2 wires) . As they age they tend to shut down the units at a lower box temperature. Since our units are known for low airflow through the air box since all outlets are generally not used, it can become an issue. It is an easy check using a jumper.
Hope this helps.
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