Implemented some code to either move a breakpoint to the next line producing some byte code 
or give a warning (configurable).

Implemented with changeset 24daea9ad41b.

Would it be possible to somehow detect such situations and warn user that breakpoint is not possible at this line?

Inspecting the generated code for Python 3.9 with the Disassembly Viewer shows, that line 6 
of the test script does not generate any code. This causes a breakpoint on this line to be 
'inactive' because the Python interpreter never ever reaches any code associated with this 
line.

I've just tested again - it works with python 3.6 and 3.7 but does not work
with 3.8 and 3.9.

Works for me. Just tested it on Debian 10 with Python 3.7.3 on my Chromebook. 
There was a similar report (issue400), which solved itself after upgrading eric.

Breakpoints do not work when set on 'while True' statement.
The attached program demonstrates the problem (see comments).