... but I have never used them to pay for SA.  

I think the biggest issue with prepaid cards is not the brand (AMEX, Visa, MC) it's the issuing bank's country.  

SA uses a non-US payment processor.  Gift cards are a HUGE target for money laundering and criminal use. So many US banks will not allow their gift cards to be used in cross-border payments, especially if the payment is NOT for a tangible good, like a toaster or furniture.  The very reason you are using a gift card for a legal activity (paying for a dating site membership) with "untraceable" funds, is the same reason that criminals use gift cards, except the criminals are buying the gift cards with the proceeds of their criminal enterprise.  

 
I don't have a solution to this, other than my suggestion to get a separate bank account and card in your own name at a different bank using an alternate mailing address. That's not anonymous, but it's not likely to be noticed by your SO.  

 
Life is good

 
The Cat