Using Jira server v7.7
Steps to reproduce:
Create a new custom timesheet and use some parameters in JQL and Issue fields
Close the custom timesheet dialog
Open the custom timesheet dialog again
Click on the new custom timesheet
Notice that it is loaded with the correct parameters set in the last step
Now change the parameters, like change the JQL and/or Issue Fields or anything else
At this point clicking Apply sounds like the most reasonable action to save your changes, but Close has also been tested. Click Apply
Open custom timesheet dialog again
Click on the custom timesheed you changed in last step
Notice that your changes have not been saved.
Problem here is that there seems to be no way of saving your changes to a custom timesheet.
A workaround would be to use the Save As, give it a new name, delete the original one, go to the new one and rename it to the original name and then configure the main menu again if you want it there. This does work, but requires too many steps.