Furnace turns off power to the thermostat
Limits are only designed to open when there's a problem, so the first step here is to find out what the problem is and fix it.  

The most common cause for a high limit to continually trip, is a dirty or improperly installed return air filter. Make sure you change the filter regularly, and that you're using one with a similar density to the one recommended by the manufacturer's documentation.  

Restricted return and supply ducts can also reduce air flow through the system, which can lead to the furnace overheating. Make sure all return air vents are clean an unobstructed by furniture and other obstructions.  Also make sure that all supply registers are open, and unobstructed.

Check the blower compartment for dust/dirt/debris.  It's not common for the blower to get dirty, but it does happen from time to time. This is especially common, when a furnace is run without a filter, or with an improperly fitted filter.

A dirty blocked up evaporator coil, could also cause restrictions. If the unit has an evaporator coil fitted, you'll want to inspect it to insure it's not dirty.  

If there's still trouble, you can check the blower motor and capacitor. Though this is only recommended if you have the proper tools and knowledge to do it. Otherwise you'll want to get an HVAC technician to handle it.

Unless you've recently changed the blower, there's not likely any problem with the way it's installed.



With all that being said.  Some furnaces are actually designed to remove power from the thermostat, in the case that a limit opens.  Obviously this design predates fancy WiFi thermostats, which require constant power to operate.  Back in the olden days, when a thermostat simply acted as a temperature switch, interrupting the signal to the thermostat was an effective solution.

Based on the schematic, it looks like the unit is controlled by the integrated furnace control module (IFC). It looks like the IFC has a separate limit circuit that it monitors, so I'm not sure that it would cut power to the thermostat if there was a problem.  In any case, the thermostat should not be damaged by losing power. I suspect there's more to this, and I haven't been able to find any service bulletins that describe this behavior. 

I'd likely start by contacting the manufacturer directly. If that doesn't provide any clues, I'd contact a different local HVAC company to come have a look.  If there's an installers sticker on the unit (or you know who installed it), and the installation company is different than the company you've been dealing with. I'd contact the company that installed the unit, as they should be quite familiar with the equipment.

Unfortunately it's difficult to troubleshoot these types of problems through the internet, especially when I'm not familiar with the equipment.