Do you have substantial spend on the card? If you just keep it in your drawer, it's less likely Amex will care about retaining you as a cardholder.

Furthermore, do you actually need to close this line? Is it hurting anything? It can be good to have lines with various credit card issuers that you can wheel and deal with (Chase is particularly willing to do this when they don't want to extend further credit but you want a new card with its signup bonus).