Can I stop visitation if my ex isn't paying support?
No. Support and parenting time are separate obligations, and violating one because the other was violated puts you in the wrong too. Withholding the children over unpaid support is not a remedy, and stopping payment because you are being denied time is not either.
Neither one is ever a self-help remedy for the other: withholding the visits, or withholding the payments, on your own decision puts you in violation too. A small number of states do let a court reduce or abate support where visitation was wrongfully denied (Missouri's statute says so expressly), but that is a judge's order after a finding, never permission to stop paying on your own.
Why the law treats them separately
The reasoning is that parenting time exists for the child, not as payment for support. A child's relationship with a parent is not a service being bought, and courts will not let it be withheld as leverage.
Support, meanwhile, is money owed for the child's benefit. It does not stop being owed because the paying parent is being treated unfairly on something else.
So the two obligations sit in separate columns. Each is enforceable on its own, and neither excuses breaking the other.
What happens when people do it anyway
Both directions tend to go badly for the person who acted.
Withholding the children can result in a contempt finding, make-up parenting time awarded to the other parent, and a note in the file about your willingness to follow court orders. That last one costs the most, because it colors how a judge reads everything else you bring, and it can influence a future custody decision. And it does not get the money paid.
Stopping payment results in arrears that keep accruing, with interest in many states though not all, plus the enforcement tools available for support, which are stronger than most people expect: wage garnishment, state and federal tax refund interception, suspension of driver's, professional and recreational licenses, liens, and reporting of the arrears to the credit bureaus, where they sit on the file that decides your next mortgage or lease. Once a state certifies arrears over $2,500, the State Department must also refuse to issue a passport and can revoke one you already hold, which people tend to discover days before a trip. For child support every state is federally required to maintain those tools, though how aggressively they are used varies, and license suspension in particular is applied in appropriate cases rather than automatically. Support debt also cannot be discharged in bankruptcy at all. And it does not get the parenting time back.
In both cases the person who reacted has converted a situation where they were clearly wronged into one where a judge is looking at two violations.
What to do instead
If the children are simply not being returned, that is a different and more urgent situation.
Enforce the one being broken. Support enforcement is well-established and, in many places, a state agency will pursue it on your behalf at little or no cost. Denial of parenting time is enforceable through the court that issued the order. Getting a decree enforced covers what that process looks like.
Document as it happens. Missed payments with dates and amounts, denied exchanges with times and what was said. Contemporaneous notes are worth far more than a reconstruction months later, and keeping a record covers how to keep one that reads as evidence rather than argument.
Keep your own side clean. This is the unglamorous advice that decides cases. Being the parent who kept paying and kept showing up, while documenting the other parent's failures, is a genuinely strong position. Being the parent who retaliated is not.
If circumstances truly changed, ask for a modification. A parent who lost their job needs a modified order, not a decision to stop paying. Support keeps accruing at the ordered amount until a court changes it, so the change has to be asked for rather than assumed, and asked for immediately. Federal law bars states from reducing child support that has already accrued, and a modification generally reaches back only to the date you filed, in some states only to the date the other parent was served. Every week of delay is debt that no court can later forgive.
The one exception worth naming
None of this means handing a child over into danger. If there is a genuine safety concern about the other parent, that is a different question with its own process, usually an emergency motion, and it should go through the court rather than through a unilateral decision. The safety resources page has help if that is where you are.
Enforcement mechanisms, how arrears accrue, and how modifications work vary by state. What does not vary is that these are two separate obligations, and that self-help remedies in either direction tend to rebound on the person using them.