Why might a Macbook Pro go back into sleep shortly after waking up?
Possibilities include (listed from the best case to worst case):


Incorrect SMC settings. To fix this: read
http://support.apple.com/kb/ht3964 (your situation is described the Power section)
A battery that's not retaining its charges. To check: read about Battery Cycle Count at http://support.apple.com/kb/ht1519


There are other possibilities but let's try these first. Feedback if these doesn't work for you.