The definition of "cohabitation" varies a lot from state to state. In some states, it means people living together and sharing living expenses. Other states require a marital, conjugal relationship.
Some courts have ruled that alimony may be reinstated when a spouse's cohabitation ends and becomes "single" again. Most courts, however, say that once the obligation to pay alimony is terminated it can never be reinstated.
This depends on the laws in your area.
Generally, alimony is tax deductible for the spouse paying the alimony and it's taxable income for the spouse receiving it. Typical monthly alimony payments are a good example. However, a court might modify the alimony order to change other types of payments so that they're "alimony" for tax purposes.
For example, depending on many factors, mortgage and other house-related payments you make on the home your ex-spouse lives in may or may not be "alimony," even though your property settlement requires you to make the payments. You may ask the court to reclassify the payments so that they're tax deductible for you and taxable income to your spouse, but usually you need your ex-spouse to agree to the change, or there must be a provision in your property settlement agreement or a state law that allows the court to modify the agreement.
There is a definite possibility she can still collect. The alimony obligation is a legal right of your ex-wife, and you're obligated to pay it.
You may, however, have a defense called "laches" (pronounced "latches"). It may be used against someone who has failed to assert a right to alimony for an unreasonable and unexplained period of time, and it would be unfair or "prejudicial" to you, the payor, to excuse your ex-wife's failure to seek payments from you.
The states differ on whether or not this defense is available, and the specific facts of each case can also defeat the defense. In many states, courts won't let you use laches as defense to back-alimony simply because you knew you were legally obligated to make the payments and you knew you weren't paying them.
It depends on the laws in your state on terminating alimony and the exact wording of your divorce settlement agreement or decree.
The alimony order may call for the automatic termination of alimony once you began cohabiting or living with the other man. Even if your order doesn't include this language, state law might include the provision. This is a very common termination provision.
However, "cohabitation" is defined by state law. Some states only require that you and the other man actually live together. Other states might require that the other man actually support you financially, while still other states require that you and the other man have a marital or conjugal relationship - you're more than just "roommates."
Alimony is usually awarded based on events that happened during the marriage. The wife staying home to raise the children, thereby sacrificing her career prospects to a great extent, is a good example. What happens to the payor spouse after the divorce usually is irrelevant to the alimony obligation.
On the other hand, however, there is certainly something to be said for the idea that the wife's sacrifices during the marriage continue to contribute to the success that the ex-husband is now enjoying. In states that follow this theory, the court may have the power to change or modify the alimony order, and so you might get an increase.
It's also possible your order "looks to the future" and includes language that allows for an increase if your husband's income goes up as it was expected to do at some point after the divorce. Again, a court may increase your alimony payments.
You really should consult an attorney in your area to figure this out. More importantly, if you are currently divorcing, ask your attorney about the alimony order.
When it comes to temporary alimony, courts in some states look at both the payor's ability to pay as well as the payee's financial need. A court isn't supposed to penalize or reward a spouse when setting an amount for spousal support.
That doesn't mean the support order can't be a tremendous burden, however. If you can't afford the order, it may be that you simply have too many bills, and you'll need to change your spending habits or life style.
It's also possible that the order is simply too large. If you gross $2000 a month and the support order is for $1200 a month, it's entirely possible that something was done incorrectly. You should probably talk to an attorney about possibly appealing the alimony order.