BoA Tried telling me the exact same thing when I called up and asked about changing my Platinum Alaska Airlines card to something basic with no annual fee (I've got the Citi AA card now, and the Citi card is the new 'everyday' card).
I've had this card for about 2 years, and got 1 plane ticket (and enough miles saved for another in my MP account) and even though I asked about converting it to a basic Visa product, the CSR told me that I'd loose all my MP miles (and I said, you mean the ones from this current billing statement, and he said no all miles I've ever accumulated with this card [almost 75k miles]).
That doesn't sound right, and he suggested that I reallocate or split (can’t remember what word he used) my credit limit between 2 cards. Even though the whole point of converting this account was so I wouldn’t have to pay the annual fee anymore. I wouldn’t want to really close this account since it’s my oldest credit card in my wallet and the limit is a lot more than all my other cards and closing it would be really bad on my credit report (oldest card and almost half of my allocated credit card credit). So I’ll call them back up and see if I can talk to someone else (unless they’re all trained to give that line) since the annual fee hasn’t posted yet (thought it would last month… guess it’s at the end of this month).