I had no trouble maintaining US accounts — I use a credit union for my primary banking needs, I also have investment accounts and credit cards — when I lived overseas, using only my overseas address. Ask around.
But one note of caution: if you think you will ever return to the US, even if you don’t plan on doing so in the immediate future, then you would be advised to keep a US address, even if it’s a family member’s address, on at least one account. Otherwise, you will find yourself in the situation we did, without a valid credit history despite having accounts continuously in good standing for 30 years with the credit union and one of the credit cards. We did finally manage to reestablish a credit history, but it was tough going at the beginning.
