Just got off the phone with Verizon.
The customer service representative had me turn on data roaming, an option in the 'Wireless & Networks' -> 'Mobile Networks' submenu. She just told me to make sure and turn it off if I'm out of the country, but in the U.S. there is no charge for roaming. She told me to restart the phone.
After doing that, in OS X I downloaded a 500 mb file, with one disconnection. I then restarted in Windows and downloaded a full 2 GB file with no problem. Got back on the phone with customer service to tell them that it seems it works fine in Windows, not in OS X. Representative said that unless my Mac is losing the actual wireless signal (which it's not), that that is not likely the culprit. She told me it would be ideal to connect with a windows and os x computer at the same time.
Lucky for me, I have two computers, both Macs, where I can run Windows on one and OS X on the other. Connected to the hot spot with both, downloading a 1 GB file on each computer at the same time, and no glitches on either operating system.
So, either the data roaming being on has solved the issue (save for the one last disconnection), or it just chooses to randomly work and randomly not. I've never been able to download such large files and stay connected for this period of time, so I'm slightly excited that it might be working now

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