If the fan on the outdoor unit is staying on, I would suspect that the system's compressor is going into what is called thermal overload.  Have another company check the charge or condition of the system.  If the condensing unit is clogged it will increase head pressures and cause the system to over heat.  It is not the t-stat as the system is still getting a call for cooling (the condenser fan is still running).  If the t-stat was bad, it would lose a call at the condenser and both the fan and compresor would drop out.  Is the small line (the liquid line in this case) really hot?  In a standard residential system the small line should only be warm to the touch (even the higher pressure 410a).  If so there may be a problem with the expansion device (if a txv type maybe the bulb is uninsulated) or a charge issue.  Get a second opinion.  Make sure that the reversing valve is still getting voltage and the system is not dropping it.