Re-titling and re-categorizing this as a Matlab Compatibility item.  The issue is that "clear all" removes everything in Octave, including breakpoints.  In Matlab, the breakpoints are preserved.  This is not a severe issue as there are easy workarounds.

As a diagnosis, the issue is that "clear all" removes both variables and functions from the symbol table.  The functions in the symbol table store the breakpoints for the function and, hence, are removed when the function is removed.

Note, Matlab doesn't recommend using "clear all" at the beginning of scripts.  As with Octave, this throws out already interpreted and compiled functions which is a performance hit when they need to be reloaded.

It is much better to be targeted.  If you have a few variables that maintain state and therefore might influence re-running a script then just clear those using "clear VAR1 VAR2" or "clearvars VAR1 VAR2".  This can be useful because if you have spent time loading a gigabyte array into the variable "data" there is no reason to clear it each time you run the script since it doesn't maintain state.

If, however, you don't want to analyze your script to determine which variables are important you could just use "clear" by itself or "clearvars" by itself which will remove workspace variables, but not affect functions and their breakpoints.

Breakpoint handling in Octave really needs to be completely overhauled.  Discussion of that job is probably best handled elsewhere.

I don't think that's expected behavior, but its not something I've noticed previously.  Which Octave versions have you seen this behavior in?

does your script start with `clear all?`