This message is generated when the final (fourth) attempt to compute the integral by the method "DoubleExponentialOscillatory" gives an error estimate that does not satisfy the precision goal.
Off[message] switches off the message; On[message] switches it on. For example: Off[NIntegrate::deoncon].
Examples
Basic Examples(1)
This shows an example of an integral for which "DoubleExponentialOscillatory" does not reach the precision goal: