That's pretty strange, this component tries several init strings for the modem, starting with AT#CID=1 and looks for an OK response. If it works its way through all 7 supported init strings it will then show the "Failed to initialize modem" error.
It sounds as though either the modem is not responding to the init string occasionally, not responding within 1 second, or the OK response is getting corrupted in some way.
Can you try this replacement for luascript\Classes\CallerIDModem.lua ?
This will provide detailed logging of what is happening