I have a Goodman furnace which is controlled by a Honeywell thermostat. Noticed problems during the daily settings especially "Leave" or "Arrive" the temperature settings aren't maintained. Example: Set for 68 degrees and the temperature will be at least 3 degrees lower. Thermostat has been replaced, same issue. Only settings working correctly are "Awake" and "Sleep".

Larry

What is the exact model of thermostat?

The new one is RTH6300B - 5-2 day model

The old one is TH4110D1007 - 5-2 day

Similar results for both. This wasn't problem initially just lately. Been in this house 2 years.

Thanks,

Larry

Here is the manual for your thermostat

http://customer.honeywell.com/techlit/pdf/69-0000s/69-1717.pdf

Here is the operator manual.

http://customer.honeywell.com/techlit/pdf/69-0000s/69-1723.pdf

Try to reset the energy star settings in the above manual. (page 16)

The thermostat is allowed to have up to two degrees slide from setting.
The thermostat that is built into the thermostat might not be posting the correct temp.
Could be dead or weak batterys.
Check over all the low voltage wiring from thermostat to furnace.

You may have done all the above since you said the old thermostat did the same thing.
Now taking that into consideration that both thermostats did this you might take into consideration a install problem.

MAKE sure that the hole for the wires that come through the wall is SEALED TIGHT.

This causes major problems because air inside the wall can be much colder than the air in the room. This will cause the thermostat to sense the in wall temperature and not the room temperature.

Now I know this thermostat is not mounted on a exterior wall? If it is move it to a interior wall.

Always make sure the batterys are installed correctly and are fresh.

You have a bit if ammo here so see if any of this helps you.