All capacitative touch screen sensors have a reduction in sensitivity when the device is not connected to ground.
When isolated from ground the device will have a capacitance to ground that is dependent upon the size of the device - for something the size of a cell-phone that capacitance is about 4pF and effectively appears in series with the touch capacitance. Your body will have a few hundred pF to ground and your finger to screen capacitance will be of the order of 1pF although if it is doing mutual capacitance detection (almost certain) the differential capacitance that needs to be detected will be of the order of 100fF.
This controller operates by scanning through the transmit channels and sensing the signals on the receive channels. It uses a mode of operation called mutual capacitance sensing where the coupling from row to column is maximum when there is no finger on the panel. Placing a finger on the panel diverts the signal to ground and can then be sensed as a touch. When the system ground is removed the signal change that results from touching the panel is reduced as there is a small capacitor in series with your finger, that reduces the touch sensitivity.
In order tolerate the large parasitic capacitances the signals will be averaged for a few seconds to get a baseline of the amount of coupling.
When the panel is touched the signal will depart from that baseline and be reported as a touch. That is probably part of the symptoms you are seeing where it changes over time.
Are there any configuration changes possible for the touch controller, frequency of operation, integration time etc? Is there any interference that is being received - when I worked on cell-phone touch sensing the biggest problem was when the phone was isolated from ground (as you are doing) or with AC adapters, but that won't begenerate interference in the case heresame frequency band as you are isolatedused for the touch sensing.