Clicking the select is what I was missing.
Can I also suggest that the line items get recalculated when the Add / Edit Budget Details pop-up is closed. It seems as though it does some of the time, but not always.
I used the same budget I outline in my first post:
1. Clicked the details button on the line item
2. Changed the charge type to Fixed and clicked save and close. The amount correctly displayed in the line item grid.
3. I Clicked the details button on the same line item
4. Changed the charge type back to Hourly and clicked save and close. The amount showed as $0.00 in the line item grid.
Once I clicked select again it recalculated and everything was fine, I think it might create less confusion if it re-calculated when the pop-up was closed.
Thanks for your help.