Siemens Auto turn-off error

Hey guys!
I have an old Siemens CX65 phone but I had to replace it with a new one because it started acting all strange.
One of the symptoms is that it switches itself off randomly with a short beep. The other thing it does is lose network coverage and switch into searching network mode without any reason. This usually happens when the phone is in a call for a minute or two. Then it just starts to make an annoying buzz out of its headphone speaker and eventually loses coverage.
Do you think this could be a software error? I am not sure if it's worth it spending money on a firmware re-install if the problem is not of that nature.