Today we're starting the beta for a new paid feature on PythonAnywhere: always-on tasks. If you have a paid account and would like to try them out, drop us a line at firstname.lastname@example.org.
With always-on tasks, you can keep a script constantly running. Once the feature's been switched on for your account, they can be set up in the "Tasks" tab -- you specify a bash command (eg. "python3.6 /home/username/myscript.py"), and the system will start running it. If it exits -- say, if it crashes, or if the server has a problem -- it will be restarted quickly.
We'd be really grateful for any and all feedback people have about this. We've been testing it internally for some months, and a private beta has been running for a while -- so we're reasonably certain it's solid and reliable, but please do remember that it is currently beta, and there may be bugs we don't know about.