A temporary fix would be to have a couple of spare Chromebooks on hand. It takes under a minute for a student to grab another computer, start it up and log in. Whatever issue that other device was having is inconsequential as long as there is a spare on hand.
Of course spares aren't always available. One option is to use Google Hangouts which have a remote desktop feature that would allow you to reach across the distance and offer a helping hand. Of course, if you're giving students access to Google Hangouts, you'll be opening up an entirely new set of issues surrounding privacy and student safety. Its a tough call. (Please don't confuse this with the Chrome Remote Desktop App. That won't work with Chromebooks. Ironic, I know.)
There is always the option of using a third party remote desktop application like AccessToGo. Depending on your firewall's settings, the particular brand of Chromebook you've procured and your bandwidth this may or may not work for you.
The take away message is this: Don't count on the kind of simple and dependable remote support you've seen from Apple and Microsoft. Chromebooks are going to be a different animal altogether.