You know, I keep on forgeting my best friend's birthday. And I have known her since she was born.
Yes,She did forget ... and I forgot her birthday this year for the first time too. Forgetting is possible - if you really want it!
Correct me if I am wrong but in the proper English one forgets ABOUT something (if it's an event, something non-material etc. - or a person even).
You can forget (meaning 'leave behind' because you're a forgetful one) , your keys or toothbrush - but i don't see how you can forget a birthday. Leaving it on a shelf or somethig?
Therefore translating OLVIDAR MI CUMPLEANOS as FORGET MY BIRTHDAY is at least a clumsy English, even if it seems to be grammatically correct (acceptable rather, and barely).
But even then it's hard to understand why the translation FORGET ABOUT MY BIRTHDAY is considered incorrect? Are we supposed to translate word for word? I admit there is no DE (or whatever) in the Spanish sentence - but I don't think distorting English will help much in learning Spanish.
Whilst I believe "She is going to forget about my birthday" should be accepted, I also think that "She is going to forget my birthday" is perfectly proper English. The reason is because of the verb "to forget" which, it seems, from your definition implies that events simply get their details lost via forgetting; however, it is an arguably equal interpretation to say that events and memories are removed via forgetting. If either but not both of these were true than only one translation would be possible. But because both interpretations see use in conversation, it is reasonable to assume that both translations are valid.