1) Check the display for the word BATTERY or BAT. (Flashing) on the display. Battery flashing or blinking on the digital display indicates low batteries. If the batteries have recently been changed and the thermostat continues to indicate low batteries, use a pencil eraser to polish each of the battery contacts inside the back of the thermostat. Do not bend them up and down when polishing or you might break them. When complete, they should all be as shiny as a mirror. This will assure proper battery back-up, allow the back light to work correctly and remove the flashing battery symbol from the screen. Battery (Solid) on Display The battery symbol (not blinking) indicates a loss of power (24 volts) from the heating and cooling equipment to the thermostat. Normally the heating and cooling do not operate when the battery indicator is on. If the battery indicator is on, check the fuses or breakers, make sure the furnace is switched on, and verify the blower compartment door is closed properly. The battery display is designed to indicate the thermostat is running on batteries, so replacing batteries has no effect on the indicator.
A beep often is provided as audible feedback when keys are depressed on many thermostats. You should check to make sure that no key is stuck in the "in" position or is otherwise activated.
2) Another possibility is that the inside compartment of the thermostat has dust. You can purchase an aerosol can of Endust for Electronics. This is a moisture free safe aerosol can of air specifically used to clean sensitive electronics such as computer keyboards, etc. These are sold at any local Walmart, KMart or Best Buy for around $5 per can.
3) 1F80-51 comes up as an obsolete model on their website and references a newer model number. Upon viewing the instruction sheet, there is no info regarding a chirping noise. The only explanation for the batteries is the types to use and how often to change them, etc.
Here is the link for the newer model that is referenced: