As a Canadian who has native US credit cards and has never even actually lived in the United States, I can tell you that it is absolutely possible to carry US credit cards while not being resident in the country.
You will need a couple of things:
- You need a US mailing address. This is absolutely required, even if you are not receiving paper bills. At a minimum, this is where replacement cards will be mailed, and where regulatory notices will be sent, if US law requires that they be mailed to you. Note that US credit card issuers are not obliged to send anything to you out of the country; it will be your responsibility to get cards forwarded to you, if you cannot return to pick them up.
- Your credit card issuer needs to understand your situation and to agree to continue providing you credit. In my case, my card issuers are aware that I live in Canada but have a permanent US mailing address (a post office box). US law requires that the credit card issuer record a resident address on your file. In my case, my Canadian physical address is recorded. If you will still own a home in the US, this can probably be used, or the bank can record your overseas address. Note that some credit card issuers may refuse to do this, and cancel your accounts. The more temporary your foreign living arrangements, the more willing they will be to stay on your account. (In my case, although I never live in the US, I am in the US nearly every calendar month and there is enough activity that they choose to continue to do business with me.)
Also, note that while applications may, on the surface, require US residency, you are not applying. (And in my case, although I am not a US resident, my credit card issuers were clearly aware of my lack of US residency - one of them, American Express, transferred data from my Canadian file, and the other, Capital One, received a copy of Canadian tax documents clearly outlining my residence and situation - and thus credit card issuers can decide to waive their own requirements if they so choose.)