Welcome to e health forum.
It is possible that, your partner might have had performance anxiety, during the initial few times, of your sexual life.
In case, your partner, is able to have early morning erections, then it would be a indicator that he is completely normal and his erection issues could be psychological.
In case, there is lack of early morning erections, it would probably be due to low testosterone levels, or due to some form of penile injury.
But, since you have mentioned, that night time sex, is completely fine, it would seem that the issue could be that he could be a night person (and not comfortable with early morning sex or other factors).
Good sex , need a prepared and relaxed brain. When in stress or when self doubt takes over, the confidence and hence the performance drops.
It is possible, that his erection may subside, when there is excess lubrication too. Though lubrication is good, as it reduces the discomfort, excess of it may reduce the feeling of fullness.
In such cases, a bit of open talk, sexual stimulation (masturbation, oral sex) and change of sexual positions and change of location will also help to improve your sex life.
I hope this helps.