Hi, English is my first language and this sentence would be said exactly as you've stated it, English is a complex language but your sentence is correct, by saying forgetting it shows that in the present tense you cannot remember something from the past this is progressively happening as it is not changing in the course of the sentence being said. Therefore it would be used in that tense. Hopefully this makes sense if it doesn't, feel free to give me a shout and I'll try to explain it a little clearer.

This sentence is fine, and it has nothing at all to do with the present tense or with any progressive form. It is in the past simple tense because it is talking about past time. The word 'forgetting' is NOT a progressive form. It is a gerund. The expression 'keep doing' is composed of the main verb which is conjugated ( in this case in the past simple) and the secondary verb which is always in the gerund form.

It depends on what the situation is. "I'm forgetting who you are" isn't correct so don't use that, however in normal sentences I would probably say "I'd forgotten who you are" However the first two can both be used as there's not much difference between the two.

1 I forgot who you were 2 I forgot who you are 3 I'm forgetting who you are Which of these three are correct?