Xero
Once you "lock" a period in Xero, we can no longer post journals as "authorised", we can only post as "draft". This is the way the Xero API has been designed, and is to protect the integrity of your Xero file.
If you need to post something from Mayday into Xero after the period is locked, you can either post it from Mayday as draft, then unlock the period in Xero and complete the posting. Or simply unlock the period in Xero, then run the posting from Mayday.
Alternatively, you can choose to post the journal at a later date from Mayday and an adjustment line will be created in the schedule so you can still reconcile back. For more information on how the adjustment line works, see this helpful article
QBO
We cannot post at all in to a locked period in QBO. If you need to post something from Mayday into QBO after the period is locked, you need to simply unlock the period in QBO, then run the posting from Mayday.
Alternatively, you can choose to post the journal at a later date from Mayday, and an adjustment line will be created in the schedule so you can still reconcile back. For more information on how the adjustment line works, see this helpful article