I have the exact same Problem! I have a MBP 2011 model with OSX 10.75.
I have also done a few hardware upgrades to this machine: I replaced the original memory with 8GB, and I installed a second 128GB OCZ SSD disc a few months ago. The SSD is the OS disc and the original disc is now my second disk.
I have the exact problem after the deep sleep, when the machine runs out of power.
From Mark’s tip, I replaced the new 8 GB RAM back to the original 4 GB RAM, but the problem remains! I assume it is a problem of the OCZ disc. I tried to update the used firmware but I failed as I need a Windows OS to do so.
So I made a workaround: I entered in the Terminal:
$ sudo pmset -a hibernatemode 0
This means that the laptop will never enter DeepSleep (or hibernation, that is the RAM is always powered and in the event of a power loss the state is lost), and in this case the sleepimage /var/vm/sleepimage can also be removed.
Orginial Article: http://linuxtoosx.blogspot.com/2011/10/optimizing-mac-os-x-for-ssd-drives.html
It is no solution for the problem but a workaround to avoid the deep sleep. But this means that your work will not be recovered after shutdown from low battery.
It should automatically reconnect but it might take a couple of seconds, more depending on the speed of your wireless router. How long are you waiting?
It will automatically join a network if you have configured it to remember networks you have previously joined. You can check this in the System Preferences>Network page. Click on the WiFi entry then on the Advanced button. In the Wi-Fi tab is a list of Preferred Networks. Make sure your network is listed, with the correct security mode. If it is listed but not at the top, perhaps the laptop is trying other networks first. Move your preferred network to the top of the list.
If that still doesn't work, try deleting it from the list, click OK, click Apply. Then turn off the Wifi by clicking the "Turn WiFi off" button above. Then turn it back on and choose your network, making sure that it is set to remember. Save/Apply and close the System Preferences and try sleeping again.
Best Answer
System Prefs > Energy Saver > Schedule