I am a Premier Exec with UA, but have now been crediting to bmi. What I do, and I suppose it would be the same for those who have purchased E+ access, is I book under my UA Mileage Plus number to have access to those seats and once at the airport on the day of departure, I go to any "online check-in" machine and change the earning to bmi. I never lose my seat this way. I think 24 hours before departure the flights are released to "airport control", so my guess is at that point no one will change your assigned seat regardless whether you still qualify for E+ access or not.
Regards,
Angeleno228