Can't publish model to Analytics manager

Just 100% confirming, but the current version of ATE that you're using is the "r3" version which we updated on the DevPortal last week, correct? (cmorfin, sorry if I failed to update you that we changed out the ATE version.)

A few other notes:

1) DockerMachinePTC *must* be running, since you're able to access ThingWorx Foundation itself. Without DockerMachinePTC running, you'll never get a response when you go to 192.168.99.100:8080. 

2) If you're not seeing DockerMachinePTC running in the VirtualBox GUI, then it's almost certain that you opened VirtualBox without doing so as Administrator. I've done so myself on multiple occasions, and it's always confusing. Long story short, everything in ATE/TTE runs on the Administrator account. If you check (via GUI or CLI) as a non-admin user (even one with admin privileges), then you'll get a response that DockerMachinePTC isn't running... even though it obviously is because you can bring up Foundation and the Analytics Mashups for Builder and Manager. 

3) Also, ThingPredictor has a pretty short timeout. For instance, if you got ATE to install correctly on day 1, but then didn't try and set up an Analytics Provider until day 2, then it's probably timed out and won't connect. For that matter, it appears that ThingPredictor may not always startup on its own whenever you stop/start ATE (for shutting down your computer, for instance). In either instance, you'll need to open cmd.exe by right-clicking and selecting "run as administrator", and then issuing the following command:

docker-machine ssh DockerMachinePTC docker restart predictionms

This is discussed on the following page in the troubleshooting section:

https://developer.thingworx.com/resources/guides/operationalize-analytics-model/analysis-provider

However, you've been so thorough in troubleshooting everything else, I have my suspicions that you've already tried this. 

If that is the case (and ThingPredictor is *STILL* not connecting), please let us know.

In which case, trying out the mods suggested by cmorfin would definitely be the next step (though those should not be required in the r3 version of ATE).