As per CSI Analysis Reference Manual, Chapter "Nonlinear Static Analysis > Important Considerations", nonlinear static analysis does not always guarantee a unique solution for models with certain characteristics. For such models, you can change it to a direct-integration time-history analysis and apply the loads quasi-statically (very slowly).
The above approach can be applied as follows:
(1) Define 10sec long ramp time history function that will ramp the load to its full value over of period of 5 seconds and then hold the load for an additional period of 5 seconds.
(2) Create a copy of your nonlinear static load case, change it to nonlinear direct-integration time-history load case.
(3) Set the time step size to 0.1 seconds and number of steps to 100 (this will correspond to a total duration of 10 seconds).
(4) Specify small damping (corresponding to 5% of modal damping).
(5) Run the time history load case and check that it has converged.