Are you sure the outlets that you mentioned are wired into the transfer switch? That would be the first thing that came to my mind. I ran a forced hot air oil system and a frig plus a fish tank on a small 2000 Honda back in the '08 ice storm without issues. But when I finally did add a transfer switch so I didn't have to wire the 2000 in every time I lost power, I only put one bank of lights in the entire house on it. Figured that lanterns were easy enough and would rather have other things on the switch seeing it was limited to 6 ( or 8, I can't remember) circuits at that time.
Or as someone else mentioned the wiring is bad and you run half of the outlets. My work actually had that happen years ago when a transformer burned out, half the lights worked and only 1 of the 2 plugs in the outlet worked. Weirdest thing I ever saw before I knew what was going on.
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