Nokia 2600 time display
I'm a cell phone sales representative and I came across a customer that had a similar problem.
What I found with her, she had so many icons displayed along the top row of the phone that the phone simply did not have room to display the time.
By clearing out her text message inbox, the sent messages, the outbox and being sure all of her voicemails had been checked, a number of the icons disappeared off the top of the screen and so the phone started to display the time again.
So that solve the problem for her. Hopefully it can help you as well.