Does a woman who doesn't keep ties with her relatives because they live far away and she doesn't have the money to do so incur sin?

There is no obligation in Islamic law except what is within one's capacity. If you are truly unable to maintain ties of kinship through money, visits, or phone calls, then this obligation is waived for you, and there is no sin upon you until you regain the ability. Maintaining ties of kinship can be through money, helping with needs, averting harm, a cheerful countenance, and supplication. The comprehensive meaning is to extend as much good as possible and avert as much harm as possible, according to one's capacity. The duty of maintaining kinship ties is according to one's ability, whether through visits, writing, or telephone.