There is no specific amount of time that a node is required to remember your transaction. Some might drop it within a few hours, others might wait a day, some nodes might remember your transaction for a week.
Actually in Bitcoin core 0.12 the "-mempoolexpiry" parameter was introduced which is set to 72 hours by default. So majority of 0.12 users will drop the transaction after 72 hours. Though anyone can re-broadcast the transaction so I can't see the use of this parameter.