How long do we try to send SMS to customers when the phone is switched off?

If a phone is switched off or has no coverage, SMS are placed in a queue where they wait for delivery until the phone becomes available again.

The time for this is not something we control but is up to each individual mobile operator how long they try to send the SMS (usually 72 hours) 
This time can be further shortened by the fact that mobile phones also usually have a setting for a maximum validity period where they do not retrieve SMS that are older than what the validity period is set to.