I experienced this behaviour to, running OctoPrint : 1.3.11rc3 and a customized version on my Prusa i3 MK3 3.7.0.
Because Prusa announced problems with "busy" processing especially during z-calibration and when the MMU2 experineces a load failure and because Prusa claimed there was a fix for that, I run the Prusa 3.7.0 with this fixed merged into it. The pull request is here: https://github.com/prusa3d/Prusa-Firmware/pull/1713
Another PR decribes pretty much the symptons of the problem I have, this is here:
https://github.com/prusa3d/Prusa-Firmware/issues/1630 There, even downgrading does not help, only a XYZ calibration.
I did disable the firmware updater, this had no effect at all.
My serial log is similar to other posts, octoprint doe not get a response and times out. The timeout is not unreasonably short: there simply is no response. This is my serial.log, it seems to receive one "start" for the printer and then no resposnse anymore.
Personally I suspect the printer, not Octoprint. Will investigate further.
2019-05-06 23:48:43,421 - serial.log is currently not enabled, you can enable it via Settings > Serial Connection > Log communication to serial.log
2019-05-06 23:52:52,498 - Enabling serial logging
2019-05-06 23:52:59,402 - Changing monitoring state from "Offline" to "Detecting serial port"
2019-05-06 23:52:59,443 - Serial port list: ['/dev/ttyACM0']
2019-05-06 23:52:59,443 - Connecting to: /dev/ttyACM0
2019-05-06 23:52:59,458 - Changing monitoring state from "Detecting serial port" to "Opening serial port"
2019-05-06 23:52:59,462 - Connected to: Serial<id=0x6c050390, open=True>(port='/dev/ttyACM0', baudrate=115200, bytesize=8, parity='N', stopbits=1, timeout=10.0, xonxoff=False, rtscts=False, dsrdtr=False), starting monitor
2019-05-06 23:52:59,463 - Changing monitoring state from "Opening serial port" to "Connecting"
2019-05-06 23:52:59,569 - Send: N0 M110 N0125
2019-05-06 23:53:11,763 - Recv: start
2019-05-06 23:53:11,784 - Send: N0 M110 N0125
2019-05-06 23:53:41,808 - There was a timeout while trying to connect to the printer
2019-05-06 23:53:41,829 - Changing monitoring state from "Connecting" to "Offline"
2019-05-06 23:53:41,869 - Connection closed, closing down monitor