I like to log a programs output \'on demand\'. Eg. the output is logged to the terminal, but another process can hook on the current output at any time.
The classic
If you can install screen on the embedded device then you can run 'myprogram' in it and detach it, and reattach it anytime you want to see the log. Something like:
$ screen -t sometitle myprogram
Hit Ctrl+A, then d to detach it.
Whenever you want to see the output, reattach it:
$ screen -DR sometitle
Hit Ctrl-A, then d to detach it again.
This way you won't have to worry about the program output using disk space at all.