Do I have Protection if I Cancel my AMEX?

Minx

Hi
I booked a couple of flights with AMEX that were due to fly back in March with different companies.  I didn't hear a single peep from one company so applied to AMEX to get my money back, which they did.  I have had some communication (automated) from the other company (BudgetAir) saying that refunds are taking a while to process and they have to wait for the airline to refund them so I thought I'd give them the benefit of the doubt and see what happened.  The problem is that I need to cancel my Amex in June or I'll have to pay the annual fee.  If I cancel my card would I still be covered if the company don't come through with the refund?
Realistically, how long should we be waiting for these companies?  Should I ask Amex to try to recover my money now?  [I did have another flight booked in May. Even though I booked through a 3rd party, AirCanada responded and gave me a 24month voucher straight away; I didn't push for a refund as I thought this was very generous given I'd booked through a 3rd party and am (relatively) happy they wont go bust - this just shows that the Airlines themselves are responding relatively quickly which casts more doubt in my mind on the 3rd parties.]
Thank you in advance for any help
(I did post this on someone else's post in an attempt to reduce traffic but i probably wasn't really relevant there; apologies if I've misplaced it and it should go elsewhere?)

D3xt3r5L4b

What card is it you have with Amex?

Minx

D3xt3r5L4b said:

What card is it you have with Amex?

I have a Preferred Rewards Gold Credit Card.  

D3xt3r5L4b

Same - my renewal has come around and because I’m not travelling for work anymore I asked what they could do reference the fee and they offered to change the card to the free Rewards Credit Card.

This will retain the card number and also continue membership points earning (1 point per £1 spent) and the fee from the Gold Card will be refunded pro-rata.

Give them a call but make sure you call during normal hours to speak to the Brighton staff as the US/overseas staff don’t provide any retention offers but the UK based staff
will. 

You can then apply for the Gold Card again at a later date and get another 12 months free (albeit without the welcome points bonus). 

Minx

Oh thank you so much! I never even considered switching to a different card! That’s another huge weight off my mind! Thank you so much! 

D3xt3r5L4b

No worries.

Just make sure you speak to the Brighton centre to get it processed correctly.

The other call centres will advise you to apply for the free Rewards card then cancel the Gold card after.