I designed system thats monitoring batteries discharging.
There are a lot of batteries sampled by AMP03 (Unity gain, diff. amp) then transfered via 2 analog 32-1 MUX (ADG732) and analog MUX 2-1 (ADG1219) and finally driven through the another unity gain amp to NI A/D in the PC.
After some months of working the battery sample amps started to burn up at random order.
May I miss anything in the design, espessialy in AMP-MUX interface?
I would tend to disagree with Harry that the inputs will float. The battery will be connected to ground through the internal 50k resistance from +IN to REF. In a steady-state condition, the positive input of your AMP03 would be at 1.5V and the negative input would be at 0V, and 30µA will flow out of the -IN, through the battery, into the +IN, and through REF to ground.
I would look to the relays and switching currents for the issue (i.e. monitor the AMP03 inputs for transients with a scope). 1) When you switch your relay, mutual loop inductance could couple the inductive spike into the inputs, which could damage the AMP03. 2) You're switching from ~0 to 1A through the battery almost instantaneously. This will create an L*dI/dt inductive voltage spike based on ESL of your power resistor and parasitic inductance. In either case, these could damage the parts over time with many repeated spikes, explaining why they operated for a while before failure.
If possible, ground the negative lead of the battery to avoid common-mode transients. Even so, you likely still need TVS or MOV protection for the AMP03.
If you spin the board, you might consider switching to an over-voltage protected instrumentation amp like the AD8226 or AD8422. The robust and nominally high impedance inputs will ease the design of external protection circuitry. Of course, you would need a ground-return for the inputs as Harry explained.