Honeywell RTH7600, RET97C has been operating good until recently. AC had always come on when there was a 1 degree difference between setting and room temperature.

You hooked it up wrong, guess you know that.

Yes there is a one degree tolerance, in fact my heater just kicked on and it is set to 67 and the inside temperature reads 67. It is also a Honeywell.

You have incorrectly wired the stat.

If you are talking about the difference between heating mode and cooling mode and the room setpoint, you can not change it. It comes from the factory with a 3 degree difference. In other words if you raise the heat setpoint until it is within 3 degrees of the cooling setpoint, for every degree you raise the heat setpoint the cooling will raise a degree.
About all you can do is increase the distance between the heat and cooling setpoint. To do this either lower the cooling setpoint to 3 degrees higher than the heat setpoint you want and then increase the cooling setpoint the desired setting. For example heat and cool setpoints are 67 and 70 respectively, and you want 65 and 73. Lower the cooling setpoint to 68 and then raise the cooling setpoint to 73. Now your heating will come on 3 degress lower than 68, the 65 you wanted and cooling will come on at 73. Remember, the thermostat new setpoints will turn on the cooling at 75 and turn back off at 73 and heat will turn on at 63 and turn off at 65.
You can perform the same using the heating setpoint, just have to look at it backwards. If you need to lower the difference I recommend a 8000 series thermostat. They are the most functional thermostat that Honeywell makes, be in mind they are about 3 times more expensive and many of the setting require a well trained tech to interpret and set properly.
Hope this helps.

Unless you just installed or had the thermostat installed recently, I would not point at the thermostat as the problem. With what you have described I would suggest have your units serviced as it sounds like a loss of charge, or failed defrost control board. The "Aux" comes on when the unit is using secondary heating (electric heat strips). That occurs when the demand temperature (what you set it to) in Heat mode is more than the current room temperature, usually ~2-4 degrees higher. Also happens in defrost mode. Defrost is a heat pump cycle that melts any build up of ice on the condenser unit (outside unit). That process is simply the unit running in cool mode which will heat up the outside unit to melt any ice. Defrost cycles vary with manufacture but usually you can tell if is in defrost by looking at the outside unit, during defrost the unit will be warm or hot sometimes there is steam and the compressor will be running but not the fan. Defrost only happens on heat pumps in "Heat" mode. Rheem has a 10 yr compressor and parts warranty, so call the installer or Rheem authorized service company.

You didn't include a model number, so it's hard to know for sure - but I'll take a stab at this one. Many of these t-stats have a programmable offset to reduce "hunting". This can be as little as 1 degree or more than 2 degrees.

This means if you set the offset to 1 degree and the room temperature to about 65 degrees, the furnace will heat the room until the t-stat registers a rising temperature of 66 degrees. The furnace shuts off and will not turn on again until the t-stat registers a falling temperature of 64 degrees. The average is 65 degrees, and prevents the furnace from starting and stopping numerous times instead of just once with the 1 degree offset.

You can further reduce the number of furnace start and stops by increasing the offset to 2 degrees. This would work like this when the t-stat is set to 65 degrees and the room is cool:

Room Temp Furnace
63 On
64 On
65 On
66 On
67 On
68 Off

The room is now warm and heat or furnace is off. The room begins to cool like below:

67 Off
66 Off
65 Off
64 Off
63 Off
62 On

With a 1 degree offset, the room temperature varies +/-1 degree (about 2 degrees total). With a 2 degree offset, the temperature about varies +/ -2 degrees (about 4 degrees total).

Also, when the thermostat shut the heat off, the heat that was made is delivered to the space instead of wasted by sending outdoors - so the room will get a little warmer even though no fuel is being burned. The same holds true at the other end. When the t-stat turn heat on, fuel is burned, but there's little heat until the source has reached the optimum temperature and then the heat is delivered to the space.

I hope this helps & good luck! Pleas rate my reply - thanks!

If you have instructions go into installer setup to match your system.. Your problem may be adjusted by going to function 5.

thats becaue you need more than this zone working like you said about the master/slave this zone is a slave.

Turn up your outside thermostat in the outside unit.
You should have about 3 degrees difference in one stage to the next. So I would change the thermosat with one that has three stages of heat.