I've used it with a cover and it still dropped out the same as when the protective cover was off. A bit of fabric or plastic isn't really going to affect radio frequencies (hence why you can put plastic in a microwave and it doesn't heat up - the Z-lynk system operates at 2.4Ghz which is the same RF frequency as a microwave and many other ISM - Industrial, Scientific and Medical devices operate on), the issue is clearly within the PCB.
Link to Axiom FCC filing photos attached showing TI module and antenna placement.