Op amp - symptoms of latchup?
There are two disparate meanings for 'latchup' in op-amps. 


Some op-amps experience a phase reversal when the common mode range at the inputs is violated. For example, if you pull a non-inverting input below the negative supply voltage by more than a few hundred mV the output may snap to the positive rail. That can cause the output to latch in that state depending on the nature of the feedback. If the current is limited, this condition typically disappears when power is cycled (unless the conditions are repeated). There's nothing in the datasheet that indicates that happens- but the makers don't always advertise it. 
CMOS circuits can experience latchup meaning that the parasitic SCR structure turns on and draws excessive supply current. If enough current is available that can be destructive. Modern circuits are pretty resistant to this and you would have to hit it with tens or hundreds of mA outside the supply rails to get that to happen, most likely, however it will not likely operate properly if you are hitting it regularly with such inputs. No maximum current is given on the datasheet that I can see. Note this: 



  Note 2:
   Connecting any terminal to voltages greater than V
  +
  or less than
  V
  –
   may cause destructive latch-up. It is recommended that no sources
  operating from external supplies be applied prior to power-up of the
  LTC1150.



Not really latchup, but spikes on the pins can can cause internal capacitors to fail, which will generally cause the output to rail. This is permanent damage. 


The usual way of dealing with the first two problems is to add some series resistance if necessary and use Schottky diodes to shunt current away from the circuit. Schottky diodes have significant leakage so you may have an issue with them. You can also look at clamping using biased diodes or BJTs, but there still may be a trade-off between leakage and clamp voltage for a given clamp current. Active circuits are more ideal, but may not be fast enough. 

Adding resistance after the clamp will help too, however it does increase the noise etc. Dividing down the input voltage after the clamp will definitely help (the absolute maximum input voltage is 300mV beyond the rails) but that op-amp is horribly noisy as it is. 

Edit: looking at your added schematic, you could try back to back Schottky diodes from the inverting input to ground (not the supply rails). Something like a BAT54 dual should be adequate and should have minimal effect on the circuit.

Also, make sure that the behavior you are observing is not a high frequency oscillation of some kind - from the limited information this seems like a strong possibility to me.