This message is generated by the method "GlobalAdaptive" before it stops the integration in the cases when the global error estimate oscillates too much. The global error is expected to decrease monotonically after a certain number of integration steps. The message is given after NIntegrate::slwcon.
Off[message] switches off the message; On[message] switches it on. For example: Off[NIntegrate::eincr].
Examples
Basic Examples(1)
The global error fails to decrease monotonically in this example:
Increasing the working precision fixes the problem: