Welcome to the Orchid Board!
Have a look at this entire thread and all my posts therein:
Eulophia petersii
I knew the people who brought Eulophia petersii into cultivation in the US years ago. Cactus and succulent growers have forgotten what they were taught about this plant, forgotten how this grows, and do not water/fertilize it enough in the summer. It has a strongly seasonal growth pattern and doesn't grow during the Winter.
A one pseudobulb division is fine for propagation, should grow strongly the next season, but would not likely flower until 2026. If your pseudobulb was divided and repotted recently, it probably has a minimal root system, and if you don't water at all this winter, it will lose those few roots. Follow Roberta's advice and water it every few weeks through the Winter.
Where do you live? When does it get warm in Spring? When the weather warms up, keep it as warm as possible, and water regularly. It will begin making new growth from the base along with new roots. It tolerates outdoor Phoenix temperatures over 110 F / 43C
and higher with no problems. I must give some shade but people in cooler climates, like southern California, can grow it in full sun.
I realize it's difficult to do the opposite of what you may read online, but once this plant begins growing in Spring, it should not dry out until all growths are mature the next Fall. It comes from grassland and gets plenty of summer water in habitat.