Can the amount of money I lent from Zakat be considered as such, given that two years have passed without it being repaid due to the borrower's poverty, or must it be demanded?

If the woman is poor or indigent and you intended the money given to her as Zakat, then it is considered Zakat, and it is not permissible to demand it back from her, because she is among the recipients of Zakat. However, if she is wealthy or you did not intend it as Zakat at the time of giving, then it is not considered Zakat. If she is poor now, it is advisable to forgive her and consider the money as charity. Otherwise, you may demand it from her when she becomes able, for Allah the Almighty says: "And if there is any debtor in difficulty, then grant him time till it is easy for him to repay, and that you remit it as charity will be better for you if you did but know."