The cohabitation in and of itself does not automatically terminate the spousal maintenance obligation; however, if their cohabitation results in a reduction in her monthly expenses (e.g. if he is contributing toward the household expenses and thereby reducing her expenses), then you may be able to ask the judge to reduce the obligation based on a substantial and continuing change in circumstances. I recommend you speak with an attorney who can discuss your options and help you decide your best course of action.
** This response is provided as general information only and does not constitute legal advice or otherwise establish an attorney-client relationship. **
You must show that there is a substantial and continuing change in circumstances that would justify a modification. For example, if the live-in boyfriend has contributed to her expenses and it appears that such contribution may continue for quite some time, then its possible this could be construed as a substantial and continuing circumstance.
It's simple. If your decree includes a cohabitation agreement then it governs. If it does not then termination can only happen for the reasons set forth in your agreement or by law, for death of either party or remarriage of wife.