My mare, Animal Crackers, does not show up in the race entry dropdown menus but I can enter her via the Upcoming Races on her profile page. She’s been in training for a few weeks in England, not boarded or in transit, etc.
Example races I can’t enter her in:
APR 4: 41 England 9.5 furlongs NW3 Allowance for 3yo+ (Turf)
APR 8: 39 England 8 furlongs Allowance for 4yo+ (Dirt)