Try following the following steps to reset your Mac mini's System Management Controller (SMC), the electronics on your logic board which control your computer's power state (see http://support.apple.com/kb/HT3964):
- Shut down the Mac mini.
- Unplug its power cord and wait 15 seconds.
- Reconnect and wait 5 seconds.
- Switch the Mac mini on.
If that does not solve the problem, there are a few possibilities:
1) I know it's obvious, but have you checked that "Schedule..." in Energy Saver Preferences is not accidentally set to shut down?
2) What is the power supply to the Mac mini's power adapter like? I have seen a few rare instances where power supply issues can cause the SMC to get confused in these cases. You could try using a known-good power supply and/or swapping to a less loaded power socket. I know it sounds unlikely, but I have seen at least one occasion where this solved strange sleep/wake behaviours of Minis.
3) Finally, the worst case is that your logic board is faulty.
If you've done all of the above and have no luck, bring your Mac mini and its power adapter to your local Apple Authorised Service Provider or Apple Store for hardware diagnostics.