Hi,

It all seems so strange. It is really difficult to comment without having the schematics and the code handy. If you are using Brownout reset enabled then you can try disabling it. If that solves the problem then there is something wrong with your PS. Also take care that all your VDD/VSS pins (11/12<->32/31) are hardwared. Although they are internally connected you cannot give power to one and draw out from the other.