After being granted permanent residency/green card; how long do we have to stay married in order for USCIS to prove marriage was bona fide?

There generally is no period of marriage duration specified in the immigration statutes and regulations, and the USCIS examines each marriage on a case-by-case basis to determine if the marriage is bona fide or is fraudulent and entered just to get immigration benefits. The USCIS generally should be persuaded of the genuine nature of a marriage where the couple has been married for 14 years and has a biological child together, but where the spouses live in separate countries, the suitable documentary evidence of the marriage may be more complex. It would be wise to engage an immigration attorney who, after learning all of the relevant details about your marriage and your immigration-related goals, would be able to advise about eligibilities and appropriate supporting documentation. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.