That is because the last block of the Button1 Block sends the sms when it should trigger a ClockTimer that sends the message when you require it to.
Now, Apps do not normally work once the phone has gone to sleep, but actually the ClockTimers do when set to 'Timer Always Fires'. So you could experiment and try sending a message after, say, 10 minutes (by which time your phone should be asleep). Much depends on your Scheduling though, you can't use a timer if it is to send a message days later, but you can send same day. You might find an extension that offers scheduling:
I wanted to share it here with you just in case any of you have the same problem, I bet there will probably be tons of easier ways to do it but this is where I get.
I share with you my finals blocks, if you can not see it properly or you need something else, just ask for it!!