I'm wanting to monitor the status of my Modbus connection. 
Under the Register Diagnostics my Modbus rc shows 2 when there has been a loss of communication -1 when it is stopped and 0 when it is running fine.

How can I check the status of the Modbus?
local ClickState = mc.mcRegGetHandle(inst, 'Click/rc');
local ClickRC = mc.mcRegGetValue (inst,"Click/rc")
I've tried both of these as well as variations of this and other API calls with no change.  It all returns 0. 

Am I using the right API or do I need to do something else or add something to this?

That should work to check rc at the Modbus device or function level.

mc.mcRegGetValue(hreg) only takes the register handle as a parameter. So something like...

local hreg, rc = mc.mcRegGetHandle(inst, "Click/rc")
-- check API return code
local ClickRc, rc = mc.mcRegGetValue(hreg)
-- check API return code

Checking the return codes from the API calls would tell you if the API call wasn't successful.

If you want the overall connection status then use the mbcntl/status reg:

local modbusStatusReg = mc.mcRegGetHandle(inst, "mbcntl/status")
To get the individual function status use the handle to the function return calls:

local modbusFunc0ErrorReg = mc.mcRegGetHandle(inst, "ModbusMPG/function0/rc")
local modbusFunc1ErrorReg = mc.mcRegGetHandle(inst, "ModbusMPG/function1/rc")
I attached a picture for reference of heirarchy. Your modbus connection names will be different.

So, as an example, if you want to make damn sure everything is running you could do a check like this:

function modbusIsRunning()
        -- check if connection is good
modbusRunning = mc.mcRegGetValueString(modbusStatusReg) == "RUNNING"

        -- check if function 1 is error free
        modbusRunning = modbusRunning and mc.mcRegGetValue(modbusFunc0ErrorReg) == mc.MERROR_NOERROR
       
        -- check if function 2 is error free
modbusRunning = (modbusRunning and mc.mcRegGetValue(modbusFunc1ErrorReg) == mc.MERROR_NOERROR) and true or false

       return modbusRunning  -- return all checks passed
end


 -- use the function to check if modbus is good
if modbusRunning() then
      -- do something in here
end     


Those == signs and the 'and true or false' are just flattened if statements (ternary ops like C), so you can explode them into 'if-else' statements if they are confusing to read:

-- check if connection is good
modbusRunning = mc.mcRegGetValueString(modbusStatusReg) == "RUNNING"


-- can be written like this
if mc.mcRegGetValueString(modbusStatusReg) == "RUNNING" then
      modbusRunning = true
else
     modbusRunning = false
end

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-- check if function 2 is error free
modbusRunning = (modbusRunning and mc.mcRegGetValue(modbusFunc1ErrorReg) == mc.MERROR_NOERROR) and true or false


-- can be written like this
if modbusRunning and (mc.mcRegGetValue(modbusFunc1ErrorReg) == mc.MERROR_NOERROR) then
      modbusRunning = true
else
     modbusRunning = false
end