AD8428 with intermittent floating inputs

I have been using the AD8428 to amplify fast transient signals in the 10-100 uV range with microsecond time resolution. The AD8428 so far appears ideal for this purpose with settling time less than 1 us at a gain of 2000, but I seem to have destroyed one chip as the output now always reads +6V even with inputs shorted to ground (+/- 9V supply). I have read other questions here where the fragility of the chip has been brought up so I want to take some precautions to avoid breaking more as they are somewhat expensive.

Can the AD8428 be damaged when inputs are left unconnected (i.e. floating) intermittently? My application is essentially a four-wire low value resistance measurement with a portable differential voltage probe connected to the inamp, thus the inputs are not permanently connected to the sensor. Normally, when the probe is connected to the specimen, the source is not floating in the sense that there is a bias current return path to ground through the probe in contact with specimen.

What is the recommended method to deal with intermittent floating inputs (e.g. to allow for sensors to be connected/disconnected while amp is powered on)? With other amps I have connected each input to ground via large value resistors, but while experimenting with the AD8428 I had to reduce the value of these resistors down to ~100 Ohms to avoid oscillations at the output with probe disconnected. However the low value resistors, while still large compared to the source impedance (~100uOhm) seemed to cause variable common mode errors depending on the contact between the probe (spring-loaded pins) and the specimen. Incidentally it appears I broke the amp after removing these resistors which is why I suspect that floating inputs might damage the device.

By the way I did consider the AD8421 as a more robust alternative, but at the moment I can not find it in stock anywhere.

Best regards