Does a gap between closing and my buyer reopening breach a continuous operation clause in the lease?

It can, depending on exactly how the continuous operation clause is worded and how long the gap actually is. Many commercial leases — especially in shopping centres and plazas, where the landlord cares about maintaining foot traffic and the overall tenant mix — require the tenant to continuously operate the business during specified hours, and a temporary closure around a change of ownership can technically fall within what the clause prohibits, even where the gap is short and purely transitional.

Whether this becomes a real problem depends on the clause's tolerance for brief interruptions (some allow reasonable closures for renovation, ownership transition, or similar), the landlord's own awareness of and cooperation with the timing of the sale, and how strictly the landlord chooses to enforce the clause in practice, which can vary considerably.

Because a continuous operation breach can theoretically give the landlord grounds to act against the tenant at exactly the wrong moment in a transition, it's worth flagging the anticipated gap to the landlord in advance and confirming there's no issue, rather than assuming a short closure will go unnoticed. A Treadstone business lawyer can review the clause and help manage this risk around your closing date.