A small number of users are reported to be facing a minor problem with the new iPhone 4 – the device appears to lock up arbitrarily that gives the impression that the phone battery has died down. However, such users have noticed that the phone comes back to life when the device is given a hard reset. To do a hard reset, users will have to press the Home and Power buttons down simultaneously.
The number of users reporting the issue looks to be insignificantly low. Also, the problem does not seem to be software related. Some users have chimed in noting that the issue could be due to corrupted iOS files that could be causing the locked down issue
If you are one of those users, I would suggest you to connect your iPhone to the computer, back up your files and then perform an iTunes OS restore. This process should replace corrupted files, if any, with their originals and thereby prevent future issues.
Do let us know in the comments if the solution works.