Yes Melatonin does lose it's effectiveness overtime.
However Melatonin remains pretty effective up until it's expiration date and Melatonin will remain pretty effective for 6 months to a year after it's expiration date.
The longer the Melatonin is kept after expiration the less effective it becomes so it's best to use the Melatonin within a year of expiration or before.
Melatonin that has expired is still safe to take but expired Melatonin won't be as effective as fresh non expired Melatonin would be.
If you take expired Melatonin then nothing bad will happen to you but the Melatonin that has expired might take longer to work and take longer to help you sleep.
Overtime the Melatonin after expiration loses it's effectiveness at helping you sleep so you may need to take an extra dose of Melatonin to get the same results.
I have taken Melatonin that has expired for 2 years and it still worked but I had to up my dosage by an extra 20 milligrams to get the same results as taking the recommended dosage.
All medication is safe to take after expiration but taking expired medication is not as effective as taking fresh medication before expiration as medication loses it's potency and effectiveness the longer it goes past expiration.