It's probably just triggering dormancy for the cool season. Leave it outside unless temperatures are expected to drop below 0 F. They need their rest time. Keeping them inside in warm conditions all winter will just stress the plant. Should be fine come spring.
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Right now it is growing indoors under grow lights for 10 hours a day sometimes 12. I am in southern California so the low temperature at night is about 60°F and the high temperature during the day is about 85°F the house is about 75°F sometimes closer to 80°F. The crêpe myrtles all around the neighborhood are definitely starting to go dormant, but with the tree still do so under artificial conditions? In the winter the temperature will not drop below about 40°F. Can such a young sapling handle these temperatures? They normally would not sprout until the spring so I had not considered putting it outside.
Edit to add... I live in an apartment with a west facing patio. It would only get sunlight for six hours a day if I left it outside because the first half of the day blocked by the building. That's why it's been growing inside. If six hours is enough at this age I can move it outside
Probably. Nothing's 100%, but it should be fine, especially considering you don't get harsh cold. It's a bit tender given what you've described (and looking at it), but in any case it is programmed for a rest period about now. Provided nothing munches on it and the roots don't rot, it should return, given proper moisture and light.