I would need more information to answer your question properly. Are the spousal support payments court ordered or part of a separation agreement? If they are in an agreement you must look to the agreement to answer whether remairrage or cohabitation will end your spousal support.
As counsel stated, a separation agreement may control the receipt of spousal support payments and even contravene the statutory law. So, if your Property Settlement Agreement states the conditions upon which you may cease receiving spousal support. such as upon cohabitation and/or in a relationship analogous to marriage, then you most likely will have to abide by its terms.
If you were awarded spousal support by the Court determining that you should receive the same and no contract such as Property Settlement Agreement exists, then you are most likely are bound by statutory law. Statutory law states generally that the payor ex-spouse may have spousal support terminated by proving cohabitation of the ex-spouse, by clear and convincing evidence, unless the payee ex-spouse is able to prove by a preponderance of the evidence that termination of such support would be unconscionable. See Generally Virginia Code § 20-109w, Notably, the person attempting to sever the obligation to pay spousal support arising due to cohabitation must bear a heavier evidentiary burden.
You will likely need to secure assistance of counsel for this issue.
I provide this advice as a courtesy and in general terms for information purposes only. Neither I nor my firm are your lawyers until you sign a legal retainer agreement and pay us an advanced legal fee.