Never seen that kind of problem before. What kind of thermostat do you have? I have seen some power stealer thermostats cause some very odd problems.
On another note, you let it drop down to 60, then recover to 68 inside the house?
Do a search on the site for "hetpump setback" for more detailed info, but with a setback that far, you are costing yourself far more money recovering the house to 68 than you save by letting it set back to 60. Keeping it 68 would be less expensive than what you are doing now...