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States That Limit Number of Times a Tenant Can Pay and Stay. Each of them require that a Notice to Pay Rent or Quit has been served for all prior late payments. 

State  Number of late rent payments required before landlord can send Unconditional Quit Notice
Connecticut  Two within six months
Georgia Two within 12 months

Three within 12 months, but Landlord must have won an eviction lawsuit for each prior nonpayment of rent episode* 

Massachusetts Two within 12 months
New Hampshire Three within 12 months
New Jersey Habitual failure to pay rent on time
South Carolina Repeated nonpayment of rent (Does not require prior notices)
Vermont Three within 12 months
Virginia Two within 12 months
* Tenants in Maryland can reinstate their tenancy by paying rent and court costs after the landlord has won the eviction lawsuit, but before the physical eviction. That rule is common in some other states as well.