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Some corrections:

Thank you very much for the letter of invitation you sent me, but I haven't been accepted for the first application for a scholarship. Therefore I will apply again. Could you send me a new letter of invitation for six months starting on the 1st of January 2010?

Dear Chantal
I don't see a big difference but you are our expert. I agree with you.

Merdogan, it's basically small differences, but for example 'therefore I will apply it' again is wrong.. it refers to something, while in this case you apply for a scholarschip so: therefore I will apply again (implicit: for the scholarship). I hope you see what I mean? If you add 'it' the sentence says: I will apply it again for the scholarship (where the letter is seen as an application form, which is wrong). It's the same for the other corrections I made, they're small but crucial .