I’ve seen this question asked a number of times, so I think it makes sense to provide some clarification for it.
Microsoft Band currently allows only a single daily alarm at a time. Once the alarm kicks-off, you can set another. This includes using either the Sleep Tile wake alarm or the Alarm Tile. To work around this limitation, you can keep your smartphone close by and make sure to enable the Notification Center Tile in the Microsoft Health app.
According to sources at Microsoft, multiple daily alerts and recurring alarms that exist on the Microsoft Band directly (without needing the smartphone nearby) is currently being considered for either a future firmware update or, if not functionally feasible (hardware limitations) integrated in Band v3.