Antenna mismatch?    Power supply isolation?  Reader defective eg ESD damage?

Do you see the problem with different antennas?  Do see the problem with another reader (same model)?

See it on ETSI and FCC antennas. The power supply is appropriately isolated (in a box). Yes, I do see the problem with another from a different company.

Are the power supply leads ferrite beaded?  Maybe it's getting de-sensed there.   Is the problem power level dependent?  You could do a sweep of power level, & plot failure % vs power level and go from there.  The last option would be to monitor the data on a scope to see what's going on.

I'd look at antenna tuning. What range are you getting and does the drop out change much with range?

From my experience, it can also be attributed to antenna/tag polarisation issues and surrounding material. What material is the tag placed upon?

From my experience it would depend on what are your items labeled with RFID tags. If those contain liquids, metals or similar things that might cause the problem. Other cause could be how close the tags are spatially located w.r.t. to each other. High density of tags reduces reading rate because of string mutual coupling and detuning between them.  

Radiation pattern inaccuracy loss, polarisation loss, antenna efficiency, antenna mismatch, fading are the losses apart from interference. 

This problem can be solved in two parallel ways:

- Antenna part (matching, directivity, ...)

- System part (signal processing)