Proper way to log progress and resume in Python
You may want to consider using the standard Python logging module to log in the information, and just keep the parser.

import logging

logger = logging.getLogger('repeatingApp')
hdlr = logging.FileHandler('/path/to/logfile')
hdlr.setFormatter(logging.Formatter('%(message)s'))
logger.addHandler(hdlr) 
logger.setLevel(logging.WARNING)

class RepeatingTask(object):
    def page(self):
        self.process_request()
        self.increment()
        logger.info(json.dumps([["current","key-xyz"],
                                [self.current,self.val_abc]]))