Probably not. Even if you had a "sleep mode", that would only turn off the notification sounds, the texts would come through.
The problem, would be with the providers, either from where they were sent, or with your provider. Perhaps they were doing message handler maintenance.
During high traffic hours it is common for sms to be delayed. At New Years, for example, I sometimes don't get a sent message for a day or so.
95% of the time, sms is received a minute or less after it is sent.
Also, phone numbers, are assigned in blocks, each block is assigned a specific message handler/server. Sometimes, a number is assigned to a group of servers that have issues, or are overloaded. sms is lost at times. It happens in the worst case.
If you lose a lot of sms (not delivered to you), the only option, is to change phone numbers to a completely different block.
This was explained to me by a Cingular tech friend a couple years ago.