I don't know enough of some of the terminology to know if this makes sense. Maybe someone  can comment on this theory.

After much experimentation, I discovered that my heat pump does cycle on and off at any temp under 67 and runs continuously at 68 or above. The setting is always reached and maintained no matter the degree of the setting. The contractor's man worked here again today. After taking readings on the main level's registers(temps mid 80's with drop to mid to high 70's) and below at the mechanical system, he thinks the temperature in the house is not getting warm enough to  make the stat shut off. He believes the problem is that the water from the loop is comig through so fast that the all the heat can't be extracted. The figure he gave me was the flow at 12(gpm?). This is a Climatemaster Tranquility 27 closed loop. He thinks by disconnecting one of the two pumps, the flow will slow down, more heat will be extracted, thus the stat will get higher heat from the registers to shut off the system. He arrived at this conclusion too late in the day to try anything, and he also wanted to consult a technician at Climatemaster or the contractor's dealer since he had never seen this problem before. What do my friends think?

Heat pumps are designed to operate on 3 GPM per Ton. If your heat pump is a 4 ton, then you need 12 GPM. Slowing down the flow will be counterproductive.
Is it running non stop in second stage?
Did the tstat get moved?

Time and again I see written the idea that too much water flow somehow reduces heat transfer because the water doesn't stay (take your pick) in the ground or in the heat exchanger long enough to transfer heat. This is incorrect. Water leaving quickly is replaced by other water, and heat transfer continues. In fact, extra flow improves heat transfer via increased turbulence.

That isn't to say we should try to force 30 GPM through a 3 ton system - increasing flows comes at the price of greatly increased pumping power, and these systems' pumps are quite inefficient.

3 GPM per ton is ideal for closed loop (assuming turbulence in the loop field) Increasing that to 4 GPM per ton will NOT reduce system's heating / cooling capacity. Efficiency may drop owing to increased pump power, but same or slightly greater heat will be available.

The temp drop into upper 70s suggests the possibility that blower is ramping up to stage 2 CFM but the compressor may be staying in low gear. Easy way to measure this is via a clamp ammeter on compressor lead, but that's not for an inexperienced person to attempt - lethal voltages lie therein!

Agreed. Any contractor who would make the statement about to much water flow causing the unit to not function properly does not understand how a geo works.

I will also agree with an ( but )

at low temps there is little difference, but as you increase flow rate you do by definition decrease the time the fluid has to release or absorb heat , I know that it is being replaced by more water at that same temp but for that to do you any good you need to increase the compressor/fan speed other wise your leaving gas in the tank so to speak . While I am almost 100% confident this is not the problem because the lost btuh is probably single digits .

I am always one to deffer to people who are smarter then me , and would say if the company want 4gpm per ton the installer should give you 4 gpm per ton

I wonder if heat load calcs were performed. Maybe the unit is just keeping up with the loss. Is there a hot water generator installed? Also, the down side of high flow is pumping costs and equipment wear(i.e. heat exchanger). It's all about the Bejamins!

The latest update:

After the contactor talked to their distributor's tech person, they have taken a whole approach. It would seem as though the tech advised them as you have advised me. No change in water flow was performed, the thermostat was reprogrammed with new settings, new readings were taken but have to retaken tomorrow this time with the water heater disconnected, and they were advised to up the speed of the airflow. They told me the tech said , based on the figures provided , that my system was underperforming. The stat was not moved as all feel this is not a problem. The owner of the company did a load calculation back in July that he said was based on cooling because that was the way it should be done. I have been sitting here since 5 pm with the stat set at 70/reading at 70 and outside temp at 55 but it hasn't shut off once. I read Engineer's idea about blower ramping up to stage two etc. to our service man, but he said he knew that wasn't the problem even though he had not performed the test as Engineer suggested. Now that the company tech is involved, I must remain hopeful since he has responded as you. However, I am about to hire another to take over. Keep your suggestions coming. I feel very fortunate to have interested people like you involved.

Remind us where you live.

central Indiana

To be fair, sizing for cooling is a valid concern - a system way oversized for cooling will not deliver adequate dehumidification during summer in any 'green grass' location. That said, I would expect the designer to lean a bit toward the heating load even if it somewhat exceeds the heating load in a cold climate such as Indiana, especially with two stage equipment - the lower stage will assist with proper dehu.

Geofan - I think we are saying the same thing in different ways - running water too fast through a system limits the heat a given volume of water will exchange, and is a waste of flow, if that makes any sense. I have the luxury of year round 71 degree open loop water at flows up to 5 GPM per ton without pump power from an artesian well. I generally limit it to about 1.5 to 2 GPM per ton out of respect for the water resource. Sometimes I pinch it back to a GPM per ton so as to fill the kids' pool with 95 degree water.

KO - your system should achieve an air delta T, or temperature rise, between the return and supply air, of at least 20 degrees, regardless of low or high stage. If that is not happening, something is way wrong. Is it possible system is sucking cold return air from a basement, crawl space, or attic due to a duct problem? That could explain low supply register temperature.

Unfortunately, many techs allow preconceived notions of the problem at hand to color and prejudice their on-site diagnostics and analysis. I feel your pain.