How many days after a month ends should the bank reconciliation be done?

The bank reconciliation should be done within a few days after the month ends. The reasons include1) making certain that the company's Cash account has the correct balance, and2) making sure that the financial statements for the month include all of the company's transactions. At the latest, the bank reconciliation should be done prior to closing the books for the month. The bank reconciliation might reveal that some revenues and/or receipts were electronically deposited into the bank account but were not yet recorded in the accounting records. Likewise, there might be some expenses and/or payments that were deducted electronically from the bank account, but were not yet entered into the company's accounts. Further, the bank reconciliation might reveal some errors in the transactions already recorded in the company's general ledger. To save time and to improve internal control, have the bank reconciliation be performed by someone other than the person writing the checks and/or recording amounts in the general ledger.

it can / should be done within second working day after end of the previous month.

Within the first working week on the new month.