> We just want him to feel happy about learning and feel proud of
> himself rather than taking learning as a negative experience.
So put yourself in his shoes. If someone is at you to do something, does that make you happy?
In general, I notice that girls are more eager to give right answers and do things in a particular sequence. Boys, not so much. Our son does this when he's not interested anymore. It's more fun to give wrong answers then. Doing something just for the sake of doing it didn't fit into the interesting category. However, if something has a point, like counting for a hide and seek game, then it was right on.
I would suggest trying to find activities he can apply his skills to instead of repetition and rote. I would also like to add that there are more types of intelligence than being able to memorize a large amount. People are very successful when they have skills in reasoning, or problem solving, or creative thinking. People are good at different things.
Let go of the babying the other people are doing. Your boyfriend's son is definitely smart enough to realize what they are doing and also what you are doing and he will respond accordingly. You are doing a great job. Remember there are many ways to learn other than Q&A , flashcard types of things.
-- response to your update --
The last sentence jumps out for me. Maybe he has learned that 'forgetting' gets him the attention from you and your boyfriend. I am in NO WAY suggesting not to give him that attention, but maybe give him his needed attention in other ways and this forgetting will disappear.
I also understand you spend a lot of time with him and do give him attention. The point I am trying to make is being aware of his perception of receiving attention. Search for Gary Chapman's "Five Love Languages" and you will find that acts of service are a way people feel loved. So, perhaps for him, you feeding him is his language for hearing that "yes, you really do love him".
Hope that helps