Try adding & to the end of your command.
This throws it ino the "background," so it should continue running atfer your TTY is closed.
Code
python examplescript.py &
Alternatively this works sometimes. Doesn't work with everything, though.
Code
python example script.py
CTRL+Z #this suspends the program
bg #this press enter, this throws it in the bg
Also fun trick,
I'm not sure what your python script does but if it has any outputs you can monitor them by having it redirect output to, say, /var/log/python/examplescript.log
Code
python examplescript.py > /var/log/python/examplescript.log 2>&1 &
And to check the output run
tail /var/log/python/examplescript.log
edit:
If none of this works try. I may have mis-read some o the documentation of the above examples.
Code
nohup python examplescript.py > /var/log/python/examplescript.log 2>&1 &
And to check the output run
tail /var/log/python/examplescript.log