I see a few odd things in here.
First, it looks like you are trying to split multi-line gdb commands across multiple calls to gdb.execute. I don't believe this will work. Certainly it isn't intended to work.
Second, there's no reason to try to do a "while" loop via gdb.execute. It's better to just do it directly in Python.
Third, I think the "command" line seems pretty wrong as well. I don't really get what it is trying to do, I guess call start_logging when the breakpoint is hit? And then continue? Well, it won't work as written.
What I would suggest is something like:
gdb.execute('break ...')
gdb.execute('run')
while gdb.parse_and_eval('$eip') != 0x...:
gdb.execute('stepi')
If you really want logging, either do the 'set logging' business or just instruct gdb.execute to return a string and log it from Python.