I have recently been involved dealing with CAA and AME so I will pass on what I have learned. I would get in touch with the AME who sent the letter and he/she should be able to contact the CAA and find out where your letter is in the system. The CAA should be able to tell you whose desk the letter is sitting on or if it arrived at all ( I always sent any mail to the CAA recorded delivery so you can start a paper trail )
It is impossible to contact the CAA by phone. I suggest you go to their website and use the notified email address. I would ask something along the lines of “just enquiring how my.....is progressing”. Keep the tone light and polite and always include your CAA reference number in any correspondence. I found it took anywhere between 10 to 30 days for a reply.
I would have thought you should have heard by now, altohough it can be a slow process.
It took eight months to sort out the medical problem I was involved in!
Just keep plugging away!