When changing an existing action that is set to run for a certain number of times (once or n times), the question is what happens on clients where it has already been executed: 

• Either the Action needs to be executed again (for the total number of executions), even if the Action has already been executed the maximum number of times on clients
• Or the Action shall only be executing for the remaining number of times (if any)

In other words: 

• If "Keep local exec. info" is checked, re-saving an Action will not reset the counter as to how often a particular Action has already been executed on a client - for e.g. a "Once only" Action this means that it will not run again on clients where it has already been executed, even if the configuration has changed(!).
• If "Keep local exec. info" is NOT checked, re-saving an Action will reset the counter as to how often a particular Action has already been executed on a client - for e.g. a "Once only" Action this means that it will be executed again on all targeted clients (naturally according to the Who tab and where conditions match according to the When tab).

For e.g. an Action set to run "Once only" this means that 

• With "Keep local exec. info" checked, re-saving the action will NOT execute it again on clients where it has already run, even if the configuration has changed(!).
• If "Keep local exec. info" is NOT checked, re-saving the action will execute it again on all targeted clients (according to the Who tab and where conditions match according to the When tab).