Our S/FTP deployments automatically copy the files to your remote server but do not preserve a link to the hosted git repo at Beanstalk. Instead, you could deploy by cloning the Beanstalk repo to your remote server and then each time you deploy, you would issue a "git pull" from within that repo on the server to get any changes from Beanstalk.
In order to compensate for changes made by Pagelime, you'd need a couple of extra steps before and after a pull:
1) commit any changes made by pagelime by issuing the command
git commit -am "commit pagelime changes"
2) pull changes from Beanstalk to the server
git pull origin master
3) push Pagelime changes to Beanstalk
git push master
This is the simplest workflow, and does not account for conflicts that cannot be auto-resolved between Pagelime changes and changes you make and commit to Beanstalk from your development environment.
Once you have configured and/or scripted this workflow in your preferred scripting language (ruby, python, php) you can start using Beanstalk's SSH deployments instead of the S/FTP deployments. Beanstalk can then log in to your server and your script or your commands automatically each time you run a deployment.